- HEAT ENERGY
- SPECIFIC HEAT CAPACITY
- HEAT CAPACITY AND SPECIFIC HEAT CAPACITY
- EVAPORATION, BOILING AND MELTING POINTS
- LATENT HEAT
- VAPOUR PRESSURE
- GAS LAWS
- PRODUCTION AND PROPAGATION OF WAVES
- PROPERTIES OF WAVES
- LIGHT WAVES
- REFRACTION OF LIGHT
HEAT ENERGY
Physics, SS 2 Week 1
Topic: HEAT ENERGY AND ITS MEASUREMENTS
Temperature
Temperature is defined as the degree of hotness or coldness of a body. It is the property of an object which determines which way heat energy will flow when it is placed in contact with another object. Heat always flows from a body at higher temperature to a body at lower temperature. Heat is a form of energy – thermal energy. When a body absorbs heat without changing its state, its temperature rises. Heat depends on the mass of a body and its temperature.
Heat is a measure of the total energy of a body. It is a form of energy due to a temperature difference. Temperature is the degree of hotness or coldness of the body and it is related to the energy of movement. It is a measure of the average kinetic energy of the molecules in a body. Unit of Heat is the Joule, unit of Temperature is degree Celcius (0C) or Kelvin (K).
Methods of Measuring Temperature
Our sense of touch can give us a general impression of the degree of hotness or coldness of a body. This is however not a reliable method of estimating or measuring a temperature, because the response of the human sense of touch to a temperature change tends to be influenced by its previous experience. Thus warm mater will feel cool if a hand initially dipped in hot water is transferred to it. Hence in order to gauge accurately the exact degree of hotness, an instrument called the thermometer is used. Thermometers are much more reliable instruments for measuring temperatures.
Thermometers use any physical property of a substance which varies in a known way with temperature, and is easily measurable as a means of gauging temperature. The substance of whose physical property is so used is known as a thermometric substance.
Fixed Temperature and Temperature Scales of Thermometer
Each thermometer has two reference temperatures or fixed points called the upper fixed temperature point and the lower fixed temperature point.
The Upper fixed point is the temperature of steam from pure water boiling at standard atmospheric pressure of 760 mm of mercury.
The Lower fixed point is the temperature of pure melting ice at the standard atmospheric pressure of 760 mm of mercury.
The difference in temperature between the two temperature points is called the fundamental interval (or temperature interval) of a thermometer. The calibration of this interval depends on the temperature scale chosen. There are three types of scale in current use
1. The Celcius scale
2. The Fahrenheit scale
3. The Absolute (or thermodynamic or Kelvin) scale
The lower and upper fixed points are oC and 100oC for the Celcius scale; 32oF and 212 oF for the Fahrenheit scale. The fundamental interval in the Celcius scale is divided into 100 equal parts,ech part of which defines 1 oC in this scale. For the Fahrenheit scale, the fundamental interval is divided into 180 units or degrees (oF).
The S.I. unit of temperature is the Kelvin (K) and its scale is called the Absolute or Thermodynamic temperature scale. The fundamental interval for the Kelvin scale goes form a lower fixed point of 273 K to an upper fixed point of 373 K i.e. a difference of 100 K. This interval is divided into 100 equal parts each of which is equal to 1 K. Temperature on this scale are not measured in degrees but in units called Kelvin (K). Hence the unit symbol K is written without the degree sign. The lower fixed point or the aero on the Kelvin scale is equal to -273 oC. It is called absolute zero.
Hence -273oC = 0 or 0oC = 273 K
A temperature of qoC in the Celcius scale is related to T of the Kelvin scale by
T = q + 273
The upper fixed point on the Kelvin scale 373 K or 100oC. Nevertheless a temperature change of 1 K. Thus we can for example say that the thermal expansivity of brass is 18 x 10-6/K or 18 x 10-6/oC or that a heat quantity which has a value of 100J/K in S.I. units.
The Upper Fixed Points
The upper fixed point of an unmarked thermometer can be determined using a hypsometer, a double wallet copper vessel constructed as shown below.
Types of Thermometers
A. Resistance thermometer
1.Thermometers which use liquids inside the glass are not suitable to be used for measuring a wide range of temperature. e.g. temperature ranging from -250 degree Celcius to about 700 degree Celsius.
2. A suitable thermometer which is used for the above range of temperatures is a resistance thermometer.
3. A resistance thermometer uses the property of the change in the platinum wire with a change in temperature.
4. The current flowing in the wire experiences more resistance when the wire becomes hot.
5. The change in the resistance of the wire is directly proportional to the change in temperature.
6. A milliammeter can and should be calibrated before hand to measure the temperature.
7. Its calibration of the melting limit of water and the boiling point of water at a pressure of 1 atmosphere is able to convert the milliameter scale to a temperature scale in degree Celsius.
8. Therefore, this thermometer is very accurate.
B. Thermocouple thermometer
1. An electromotive force (e.m.f.) will be produced in a thermocouple when there is a temperature difference between the hot junction and the cold junction. Once this happens, a current will flow.
2. This thermometer is very sensitive and responds towards slight change in temperature.
3. Since the physical quantity which is used to measure the temperature is the e.m.f, this thermometer can be connected to other electrical circuits to control or record the surrounding temperature.
4. A thermocouple thermometer is a very sensitive thermometer which is suitable for measuring temperatures ranging from -250 degree Celsius to 1600 degree Celsius.
C. Liquid-in-glass Thermometers
A liquid-in-glass thermometer is widely used due to its accuracy for the temperature range -200 to 600°C. Compared to other thermometers, it is simple and no other equipment beyond the human eye is required. The LIG thermometer is one of the earliest thermometers. It has been used in medicine, metrology and industry. The first thermometer appeared around 1650 and was a development from the thermoscope. The liquid used was spirit from wine. By 1714, thermometers with mercury were found to give a more linear scale than spirits. By 1742, a centigrade scale using 100 steps from the point of boiling water to the melting point of water was suggested by Anders Celsius.
In the LIG thermometer the thermally sensitive element is a liquid contained in a graduated glass envelope. The principle used to measure temperature is that of the apparent thermal expansion of the liquid. It is the difference between the volumetric reversible thermal expansion of the liquid and its glass container that makes it possible to measure temperature.
D. Mercury
1. The physical quantity that is used to determine the temperature of a body by means of a mercury thermometer is the length of the thread mercury, or to be more exact, the volume of mercury.
2. When the temperature increases, the volume of the mercury increases too.
3. The sensitivity of a mercury thermometer can be increased by
a. reducing the diameter of the capillary tube.
b. increasing the size of the bulb.
c. using a thinner-walled glass bulb.
4. Normally mercury is used in a thermometer because it:
a. Expands uniformly.
b. has a higher boiling limit.
c. is opaque and therefore it is easier to read off the temperature.
d. is a good conductor of heat.
e. does not stick to the glass.
5. One weakness of the mercury thermometer in the measurement of an accurate temperature is that the glass of the capillary tube also expands when the temperature expands.
In addition to that, it is extremely dangerous if the glass tube breaks because mercury is very poisonous.
Mercury thermometer is suitable to measure temperature between -30 degree Celsius to 300 degree Celcius.
E. Gas thermometers
There are two main types of gas thermometer, one operating at constant volume and the other at constant pressure. The constant-volume gas thermometer is by far the more widely used and so we will deal with it alone.
The ideal gas equation states that for n moles of a gas:
PV = nRT
and therefore for a gas at constant volume V the absolute temperature T is directly proportional to the pressure of the gas P.
A simple form of constant-volume gas thermometer is shown in Figure 1. The gas is enclosed in the bulb B and the pressure recorded by the difference in levels (h) of the mercury columns. The mercury level at R is always adjusted so that it coincides with the mark. The pressure of the gas within the bulb is then given by P = A + h, where A is the atmospheric pressure.
If the atmospheric pressure varies during the experiment allowance must be made for this, since it is the total gas pressure that is measured.
The gas in the bulb can be air, hydrogen, helium or nitrogen, although it is the constant-volume
hydrogen gas thermometer that is taken as standard.
The simple form of constant-volume gas thermometer is subject to errors due to changes in volume of the glass and of the mercury (due to temperature variations), to pressure on the bulb and to the exposed column ‘dead space’, that is, the volume of gas that is outside the region of which the temperature is being measured.
It has the further disadvantages that it is not direct-reading, and that it cannot be used to measure varying temperatures, because gases are such poor conductors of heat.
A more accurate form of constant-volume thermometer has been designed where some of these errors are reduced, the dead space is made as small as possible and the bulb containing the gas is large (1.6 litres).
By using different gas thermometers a wide range of temperatures can be measured:
Hydrogen -200 oC to +500 oC
Nitrogen +500 oC to + 1500 oC
Helium -270 oC to + 1500 oC
These thermometers can be very accurate, to within 0.005 oC from 0 oC to 100 oC, 0.1 oC around 500 oC and to within 2 oC at 1500 oC
The almost the length of the thermometer hangs freely in the steam in the inner chamber well above the boiling water and is placed in such a way that its mercury thread is just visible above the top of a cork. A manometer is attached to the inner chamber of the hypsometer to ensure that the pressure within it is 760 mm 0f mercury. This is so when the mercury levels in both arms of the manometer are the same. Also attached to the vessel is a steam-outlet to ensure that no steam condenses on the thermometer. The water is heated until it starts boiling.
When the thermometer has been in the steam for some time and the position of the mercury thread has remained steady, its level is marked on the stem by a light scratch. This mark is the upper fixed point or the upper temperature point.
An important precaution is to ensure that the bulb of the thermometer does not come in contact with the boiling water. The thermometer should be suspended only in the steam. Also we must avoid parallax error in locating the boiling point.
The Lower Fixed Point
The lower fixed point is determined by placing the thermometer upright in pure melting ice contained in a glass funnel when the mercury level remains steady for sometime, a mark is made on the stem of the thermometer to indicate this level, which represents the lower temperature level.
There are three modes of transfer of heat
Conduction: The mode of transfer of heat from molecules to molecules without movement of particles.. Conduction takes place in solid as its molecules ate closely packed. Solids, metals and alloy are good conductor. Non metals, plastic glass are bad conductor of heat.
Convection: The mode of transfer of heat from molecules to molecules with movement of particles. In liquids and gasses heat transferred by convection as molecules are far apart from each other.
Radiation: The mode of transfer of heat that does not require any material medium. Heat of sun reach the earth by radiation.
Question
1. These are the effects of heat except
A. Heat increases in temperature B. Heat expands a substance C. Heat changes the state D. Heat brings chain reaction
2. Mercury is preferred in thermometers, which of these is not correct?
A. It expands uniformly B. It turns solid at room temperature. C. It does not stick to wall D. It is shiny and easy to see
3. The lower and upper fixed point for the Celcius scales are (note: all in oC)
A. 0 and 272 B. 0 and 373 C. 10 and 100 D. 0 and 100
4. There are how many types of scales in current use?
A. 1 B. 2 C. 3 D. 4
5. Which is not correct as part of the types of thermometer?
A. Gas Thermometer B. Plastic Thermometer C. Resistance thermometer D. Thermoelectric thermometer
Answers
1. D. 2. B 3. C 4. C 5. B
HEAT CAPACITY AND SPECIFIC HEAT CAPACITY
Physics SS 2 Week 2
Topic: Heat Capacity
Introduction
The heat capacity measures the amount of heat necessary to raise the temperature of an object or system by one degree Celsius.
Heat capacity is defined as the ratio of the heat energy added to an object to its change in temperature.
Heat capacity is the measurable physical quantity that characterizes the amount of heat required to change a substance’s temperature by a given amount. It is measured in joules per Kelvin and given by C = Q/∆T
The heat capacity is an extensive property, scaling with the size of the system.
The heat capacity of most systems is not constant (though it can often be treated as such). It depends on the temperature, pressure, and volume of the system under consideration.
Enthalpy the total amount of energy in a system, including both the internal energy and the energy needed to displace its environment
Heat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance’s temperature by a given amount. In SI units, heat capacity is expressed in units of joules per kelvin (J/K).
An object’s heat capacity (symbol C) is defined as the ratio of the amount of heat energy transferred to an object to the resulting increase in temperature of the object
Heat capacity is an extensive property, so it scales with the size of the system. A sample containing twice the amount of substance as another sample requires the transfer of twice as much heat (Q) to achieve the same change in temperature (ΔT). For example, if it takes 1,000 J to heat a block of iron, it would take 2,000 J to heat a second block of iron with twice the mass as the first.
The Measurement of Heat Capacity
The heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system under study. In particular, it is dependent on temperature itself, as well as on the pressure and the volume of the system, and the ways in which pressures and volumes have been allowed to change while the system has passed from one temperature to another. The reason for this is that pressure-volume work done to the system raises its temperature by a mechanism other than heating, while pressure-volume work done by the system absorbs heat without raising the system’s temperature. (The temperature dependence is why the definition of a calorie is formally the energy needed to heat 1 g of water from 14.5 to 15.5 °C instead of generally by 1 °C.)
Different measurements of heat capacity can therefore be performed, most commonly at constant pressure and constant volume. The values thus measured are usually subscripted (by p and V, respectively) to indicate the definition. Gases and liquids are typically also measured at constant volume. Measurements under constant pressure produce larger values than those at constant volume because the constant pressure values also include heat energy that is used to do work to expand the substance against the constant pressure as its temperature increases. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.
Thermodynamic Relations and Definition of Heat Capacity
The internal energy of a closed system changes either by adding heat to the system or by the system performing work. Recalling the first law of thermodynamics,
For work as a result of an increase of the system volume we may write,
dU = dQ – PdV
If the heat is added at constant volume, then the second term of this relation vanishes and one readily obtains
(¶U/¶T)V = (¶Q/¶T)V = CV
This defines the heat capacity at constant volume, CV. Another useful quantity is the heat capacity at constant pressure, CP. With the enthalpy of the system given by
H = U + PV
our equation for dU changes to
dH = ¶Q + VdP
and therefore, at constant pressure, we have
(¶H/¶T)P = (¶Q/¶T)P = CP
Specific Heat Capacity
Specific heat capacity of a substance is defined as the heat capacity of the substance per unit mass of the substance. Therefore, if energy Q is given to the substance having mass m, and it results in the change in the temperature of the substance by ΔT. Hence, Specific Heat of the substance is
c = Q/mΔT
Heat capacity of a substance is denoted by C. It is defined as the amount of energy which is required to increase the temperature of the substance by 1°C.
Specific heat capacity (c) of a substance is the heat required to produce unit temperature rise in unit mass of the substance.
Specific Heat
When energy is given to a substance and the substance is not performing any work, it results into increase in temperature of the substance. (If the temperature of the substance is not increased, when the heat is given to it, and also the substance is not performing any work, it could lead to change in the phase of the substance and this phenomenon is termed as Phase Transition). Amount of heat, required to raise the temperature of a substance by a certain amount, depends on the properties of the substance and this amount of heat varies from substance to substance.
For example, the amount of energy or heat required to increase the temperature of 1 kg of water by 1°C is 4.186 J, but the amount of heat required to increase the temperature of 1 kg of copper by 1°C is only 387 J. There are two methods to increase the temperature of the substance:
1. By transferring heat or energy to it.
2. By doing Work on it.
According to the definition, if heat Q given to the substance increases the temperature of the substance by ΔT, then
Q = CΔT
Specific heat is essentially a measure of how thermally insensitive a substance is to the addition of energy. If the specific heat capacity of a substance is more, then for a given mass m of a substance, for a particular ΔT temperature change, more energy Q needs to be transferred to the substance as compared to the second substance having less specific heat capacity. Therefore, more the specific heat capacity, more energy needs to be transferred to the substance if the other conditions (Q, m,ΔT ) are same.
Formula for specific heat can be written asc =Q/mΔT
Specific Heat Units: SI unit of Specific Heat is Joules per Kilogram Kelvin. (J/kg.K).
Specific Heat Table
Specific Heat Table for some of the substances is given below at 25 0C and Standard Atmospheric pressure
| Substance | Specific Heat(J/kg. °C) |
| Specific Heat of Beryllium | 1830 |
| Specific Heat of Cadmium | 230 |
| Specific Heat of Copper | 387 |
| Specific Heat of Germanium | 322 |
| Specific Heat of Gold | 129 |
| Specific Heat of Iron | 448 |
| Specific Heat of Lead | 128 |
| Specific Heat of Silicon | 703 |
| Specific Heat of Silver | 234 |
| Specific Heat of Brass | 380 |
| Specific Heat of Glass | 837 |
| Specific Heat of Ice(-5°C) | 2090 |
| Specific Heat of Marble | 860 |
| Specific Heat of Wood | 1700 |
| Specific Heat of Alcohol(ethyl) | 2400 |
| Specific Heat of Mercury | 140 |
| Specific Heat of Water(15°C) | 4186 |
| Specific Heat of Steam(100°C) | 2010 |
| Specific Heat of Aluminium | 900 |
| Specific Heat of Tin | 540 |
| Specific Heat of Steel | 120 |
| Specific Heat of Sand | 830 |
| Specific Heat of Ethanol (Alcohol, ethyl 32°F) | 2.3 K |
Methods of determining Specific Heat Capacity
There are several simple methods for measuring the specific heat capacities of both solids and liquids, such as the method of mixtures, but we will consider here only electrical methods. Since the specific heat capacity varies with temperature, we have seen it is important to record the mean temperature at which the measurement is made.
Electrical calorimeters
Figure 1(a) and 1(b) show possible arrangements for electrical calorimeters for a solid and a liquid specimen.
The material under investigation is heated by an electrical immersion heater and the input energy (Q) and the rise in temperature that this produces are measured. If the mass of the specimen (solid or liquid) is m and its specific heat capacity C, then Q = m C (q1 – q0) + q
where θ0 and θ1 are the initial and final temperatures of the specimen and q is the heat loss. Using the cooling correction, the value of q may be found. This simple method can be used for liquids or solids, although in the case of a liquid, allowance has to be made for the thermal capacity of the container, and the liquid should also be stirred to allow an even distribution of the heat energy throughout its volume. This is necessary since liquids are such poor thermal conductors
The continuous-flow calorimeter
This was first developed by Calendar and Barnes in 1902 for the measurement of the specific heat capacity of a liquid, and is shown in diagram below. Its main advantage is that the thermal capacity of the apparatus itself need not be known.
Liquid flows in from a constant-head apparatus at a constant rate past a thermometer (θ 0). It then flows around the heater coil and out past a second thermometer where the outlet temperature (θ1) may be measured. When steady-state conditions have been reached (a temperature difference between inlet and outlet points of 50C is reasonable) the temperatures and the flow rate of the liquid (m) are measured. A vacuum jacket round the heater coil reduces heat losses.
The electrical energy supplied to the heater coil (E = V I t) may be found readily with a joulemeter or with an ammeter and voltmeter.
Two sets of measurements are carried out.
For a first experiment we have:
Electrical energy supplied (E1) = V1 I1 t1 = m1 C (θ1 – θ0) + q
C is the specific heat capacity of the liquid and q the heat loss to the surroundings and to the apparatus.
The flow rate and rate of energy input are now altered to give a second set of results. However, if the inlet and outlet temperatures are the same as in the first experiment the heat loss will also be the same. Therefore:
Electrical energy supplied (E2) = = V2 I2 t2 = m2 C (θ1 – θO) + q
Eliminating the heat loss (q) gives
Specific heat capacity of the liquid (C) = [E2 – E1]/ (m2 – m1)(q1 – qo)
Practical advice
A smaller amount of water could be heated in a polystyrene cup than in a calorimeter; this reduces the heating time needed and provides insulation. The heater must be covered by the water. The heat absorbed by the polystyrene is also small compared to that absorbed by the calorimeter. However take care that the heater does not touch the cup or it will melt. Thermometers can also overbalance the cup. Always stir liquids before taking a temperature.
It is better to choose an immersion heater that fits all the way into the solid material rather than having part of it in the air. The top of the block should also be lagged. Take the highest temperature reached by the block after the heater has been switched off.
Questions
1. The heat capacity measures the amount of heat necessary to raise the temperature of an object or system by ……………. degree celsius.
A. One B. Hundred C. Ninety D. One thousand
2. Heat Capacity is measured in
A. Kelvin per joules B. joules per Kelvin C. Joules D. Kelvin
3. The specific heat value for Aluminium in J/kg. °C is
A. 800 B. 900 C. 980 D. 450
4. Formula for Specific Heat Capacity can be written a s
A. Q/mΔT B. Qm∆T C. Q∆T D. m∆T
5. The heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system under study. In particular, it is dependent on
A. Temperature only B. Pressure and Temperature C. Volume and Pressure D. Temperature, Volume and Pressure.
Answers
1. A 2. B 3. B 4. A 5. D
SPECIFIC HEAT CAPACITY
Physics SS 2 Week 3
Topic: SPECIFIC HEAT CAPACITY
CALCULATIONS ON SPECIFIC HEAT CAPACITY
If someone increases the temperature of the substance, there will be an increase in the kinetic energy of its molecules – that is increase in its internal energy. So one needs to supply energy. The energy needed to raise the temperature of an object is proportional to the increase in temperature and mass of the object
Energy ∝ mass ×Temperature rise
Here the constant of proportionality which is depends on the substance, is called the Specific Heat Capacity (c).
So,
Energy=mass × specific heat capacity × Temperature rise
q = m × c × ΔT
The energy gained or lost as heat when a given mass of a substance is warmed or cooled can be calculated using above equation.
So the specific heat capacity,
c = q/m×ΔT
Here,
c = The specific heat capacity
q = It is the energy gained or lost.
m = Mass of the substance
ΔT = Tfinal − Tinitial = the change in temperature.
The units of the specific heat capacity are J/kgK = Jkg−1K−1.
A 43.2 g block of an unknown metal at 89.0 °C was dropped into an insulated vessel containing 43.00 g of ice and 26.00 g of water at 0 °C. After the system had reached equilibrium it was determined that 9.15 g of the ice had melted. What is the specific heat of the metal? (The heat of fusion of ice = 334.166 J g¯1.)
Solution:
Comment: this variation of the usual suspects (detailed above) does NOT involve a temperature change in the water, only in the metal. Rather, some ice melts and the whole ice-water system stays at zero Celsius.
1) Determine heat gained by the ice that melted:
9.15 g times 334.166 J g¯1 = 3057.62 J
2) Then substitute and solve for the specific heat:
q = (mass) (Δt) (Cp, metal)
3057.62 J = (43.2 g) (89.0 °C) (x)
x = 0.795 J g¯1 °C¯1
A 35.0 g block of metal at 80.0 °C is added to a mixture of 100.0 g of water and 15.0 g of ice in an isolated container. All the ice melted and the temperature in the container rose to 10.0 °C. What is the specific heat of the metal?
Solution:
1) Determine heat required to melt the ice:
q = (15.0 g) (334.166 J g¯1) = 5012.49 J
Note that the 100 g of water is not mentioned yet.
2) Determine heat need to raise 115 g of water from 0 to 10.0 °C:
q = (115 g) (10.0 °C) (4.184 J g¯1 °C¯1) = 4811.6 J
Note the inclusion of the melted 15 g of ice. Also, notice that the water was at zero °C. We know this from the presence of the ice.
3) Determine the specific heat of the metal:
(5012.49 J + 4811.6 J) = (35.0 g) (70.0 °C) (x)
x = 4.01 J g¯1 °C¯1
A piece of metal weighing 59.047 g was heated to 100.0 °C and then put it into 100.0 mL of water (initially at 23.7 °C). The metal and water were allowed to come to an equilibrium temperature, determined to be 27.8 °C. Assuming no heat lost to the environment, calculate the specific heat of the metal.
qmetal = qwater
(mass) (Δt) (Cp) = (mass) (Δt) (Cp)
(59.047 g) (72.2 °C) (x) = (100.0 g) (4.1 °C) (4.184 J g¯1 °C¯1)
x = 0.402 J g¯1 °C¯1
A 25.6 g piece of metal was taken from a beaker of boiling water at 100.0 °C and placed directly into a calorimeter holding 100.0 mL of water at 25.0 °C. The calorimeter heat capacity is 1.23 J/K. Given that the final temperature at thermal equilibrium is 26.2 °C, determine the specific heat capacity of the metal.
Solution:
1) We know this:
qlost, metal = qgained
2) However, energy is gained by two different entities (the water and the calorimeter itself). Therefore:
qlost, metal = qgained, water + qgained, calorimeter
3) Substituting, we have:
(mass) (Δt) (Cp, metal) = (mass) (Δt) (Cp, water) + (Δt of water) (calorimeter constant)
4) Putting values into place and solving:
(25.6 g) (73.8 °C) (x) = (100.0 g) (1.2 °C) (4.184 J/g °C) + (1.2 °C) (1.23 J/K)
x = 0.266 J/g °C
How much energy must be transferred to raise the temperature of a cup of tea (250 ml) from 293.7 K to 368.8 K. Assume that the tea and water have the same density(1 g/ml), and specific heat capacity (4.184 J/gK).
Solution:
Given,
c = 4.184 J/gK
Mass (m) = 250ml1g/ml = 250g
ΔT = Tfinal − Tinitial = 368.8K – 293.7K = 75.1 K
We have,
q = m × c × ΔT
= 250× 4.184×75.1
= 78.554kJ
| A 245.7g sample of metal at 75.2 degrees Celsius was placed in 115.43g water at 22.6 degrees Celsius. The final temperature of the water and metal was 34.6 Celsius. If no heat was lost to the surroundings what is the specific heat of the metal? |
| -qmetal=qwater -(mC∆T)=mC∆T -(mC(Tf-Ti))= mC(Tf-Ti) – (245.7g x C x (34.6oC-75.2oC))=115.43g(4.18J/goC)(34.6oC-22.6oC)C x (9975goC)=5790J0.580J/goC = CDetermine the final temperature when a 25.0g piece of iron at 85.0°C is placed into 75.0grams of water at 20.0°C. The specific heat of iron is 0.450 J/g°C. The specific heat of water is 4.18 J/g°C.-qmetal = qwater -(mC∆T)=mC∆T -(mC(Tf-Ti))= mC(Tf-Ti) -(25.0g(0.450J/goC)(Tf-85.0oC))=75.0g(4.18J/goC)(Tf-20.0oC) 956.25-11.25Tf=313.5Tf-6270 7226.25=324.75Tf 7226.25/324.75=Tf 22.3oC=Tf Questions 1. Calculate the amount of heat needed to increase the temperature of 250g of water from 20oC to 46oC A. 47 KJ B. 38 KJ C. 23 KJ D. 75 KJ 2. Calculate the specific heat capacity of copper given that 204.75 J of energy raises the temperature of 15g of copper from 25o to 60o. A. 400 J g¯1 °C¯1 B. 478 J g¯1 °C¯1 C. 752 J g¯1 °C¯1 D. 245 J g¯1 °C¯1 3. What is the quantity of heat required to raise the temperature of 300 g of aluminium cube from 300C to 700C? (Specific heat capacity of aluminium is 900 JKg-1K-1 23 KJ B. 34 KJ C. 10.8 KJ D. 12.9 KJ 4. 216 J of energy is required to raise the temperature of aluminum from 15o to 35oC. Calculate the mass of aluminum. (Specific Heat Capacity of aluminum is 0.90 JoC-1g-1) A. 14 g B. 10g C. 12g D. 25g 5. The temperature of a piece of Metal X with a mass of 95.4g increases from 25.0°C to 48.0°C as the metal absorbs 849 J of heat. What is the specific heat of Metal X? A. 0.49 Jg-1 0C-1 B. 3.7 Jg-1 0C-1 C. 0.39 Jg-1 0C-1 D. 4.2 Jg-1 0C-1 Answers 1. B 2. B 3. C 4. C 5. C |
EVAPORATION, BOILING AND MELTING POINTS
Physics SS 2 Week 4
Topic: EVAPORATION, BOILING AND MELTING POINTS AND THEIR DETERMINATION
WHAT IS EVAPORATION?
In liquids, the molecules of the liquid are always in a state of random motion, within its surface. Some molecules may have sufficient kinetic energy to escape from the surface of the liquid. This process is known as evaporation. Evaporation takes place at all temperatures. Rate of evaporation increases with rise in temperature and becomes maximum at the boiling point of the liquid. The process of evaporation also increases with increase in surface area of the liquid.
Evaporation is a process where a liquid turns spontaneously into vapour below its boiling point.
Evaporation requires energy. A liquid draws heat energy from the surrounding thereby cooling the surrounding.
Example 1: Water placed in a porous pot becomes very cool after some time. This is because water molecules draw energy from the water itself for evaporation and hence, the temperature of water in the pot falls.
Example 2: If we smear our hand with spirit that portion feels cold because spirit evaporates quickly using heat energy from the skin.
Example 3: During summer process of perspiration keeps the body cool. When we perspire, the sweat evaporates using heat from our body thereby keeping it cool.
Example 4: Water cycle in nature is initiated by the evaporation of water from lakes, ponds, rivers, sea, etc. Water evaporates due to sun’s heat. Water vapor rises to the sky to from clouds. Clouds condense to form raindrops, which fall on the earth. And the water cycle continues.
Molecular Explanation of Evaporation
According to the kinetic molecular theory of matter, a liquid consists of molecules that are in constant motion. The average velocity and hence the average kinetic energy of the molecules is related to the temperature of the liquid. When the temperature increases, the molecules gain more kinetic energy.
Molecules with high speed near the surface of the liquid may have enough kinetic energy to break away from the attraction of other molecules and move outside the liquid surface as molecules of vapour. Some of these molecules stay outside the liquid, some however return to the liquid due to the attractive forces from the molecules in the liquid. As more and more molecules stay outside the liquid surface, the liquid evaporates more and more. High temperatures increase the velocities of all the molecules, thus allowing more molecules to escape from the surface, hence increasing the rate of evaporation by sweeping away the molecules of vapours above the liquid surface, thus making for fresh supply of escaping molecules.
Cooling by Evaporation
Whenever methylated or petrol is spilled over any part of our body, we usually a cooling effect as the liquid evaporates. The body becomes cooler because the latent heat needed to convert the liquid to the vapour is extracted from the liquid or any other in contact with it. This extraction from of the latent heat from the liquid leads to a fall in its temperature. The faster the evaporation the greater is the fall in temperature.
The human body utilizes the effect of evaporation for cooling. Perspiration cools the body as sweat evaporates from the surface of the skin. As the latent heat of vaporization is extracted from the body, it is cooled in the process. Cooling by evaporation is also utilized by doctors from numbing pains from needle points. Volatile either methylated spirit is usually dabbed on the skin before the body is injected with some drug. As the methylated spirit evaporates, it cools the part of the skin and numbs it so that the pain from the needle prick during an injection process is not much felt.
Boiling point of certain liquids
| Liquid | Boiling point |
| Water | 100°c |
| Mercury | 357°C |
| Ethyl alcohol | 79°C |
| Methyl alcohol | 64°C |
| Glycerol | 290°C |
| Turpentine | 156°C |
Melting Point Determination
Pure, crystalline solids have a characteristic melting point, the temperature at which the solid melts to become a liquid. The transition between the solid and the liquid is so sharp for small samples of a pure substance that melting points can be measured to 0.1oC. The melting point of solid oxygen, for example, is -218.4oC.
Liquids have a characteristic temperature at which they turn into solids, known as their freezing point. In theory, the melting point of a solid should be the same as the freezing point of the liquid. In practice, small differences between these quantities can be observed.
It is difficult, if not impossible, to heat a solid above its melting point because the heat that enters the solid at its melting point is used to convert the solid into a liquid. It is possible, however, to cool some liquids to temperatures below their freezing points without forming a solid. When this is done, the liquid is said to be super cooled.
An example of a super cooled liquid can be made by heating solid sodium acetate trihydrate (NaCH3CO2 3 H2O). When this solid melts, the sodium acetate dissolves in the water that was trapped in the crystal to form a solution. When the solution cools to room temperature, it should solidify. But it often doesn’t. If a small crystal of sodium acetate trihydrate is added to the liquid, however, the contents of the flask solidify within seconds.
A liquid can become super cooled because the particles in a solid are packed in a regular structure that is characteristic of that particular substance. Some of these solids form very easily; others do not. Some need a particle of dust, or a seed crystal, to act as a site on which the crystal can grow. In order to form crystals of sodium acetate trihydrate, Na+ ions, CH3CO2– ions, and water molecules must come together in the proper orientation. It is difficult for these particles to organize themselves, but a seed crystal can provide the framework on which the proper arrangement of ions and water molecules can grow.
Because it is difficult to heat solids to temperatures above their melting points, and because pure solids tend to melt over a very small temperature range, melting points are often used to help identify compounds.
Measurements of the melting point of a solid can also provide information about the purity of the substance. Pure, crystalline solids melt over a very narrow range of temperatures, whereas mixtures melt over a broad temperature range. Mixtures also tend to melt at temperatures below the melting points of the pure solids.
Boiling Point
When a liquid is heated, it eventually reaches a temperature at which the vapor pressure is large enough that bubbles form inside the body of the liquid. This temperature is called the boiling point. Once the liquid starts to boil, the temperature remains constant until all of the liquid has been converted to a gas.
The normal boiling point of water is 100oC. But if you try to cook an egg in boiling water while camping in the Rocky Mountains at an elevation of 10,000 feet, you will find that it takes longer for the egg to cook because water boils at only 90oC at this elevation.
In theory, you shouldn’t be able to heat a liquid to temperatures above its normal boiling point. Before microwave ovens became popular, however, pressure cookers were used to decrease the amount of time it took to cook food. In a typical pressure cooker, water can remain a liquid at temperatures as high as 120oC, and food cooks in as little as one-third the normal time.
To explain why water boils at 90oC in the mountains and 120oC in a pressure cooker, even though the normal boiling point of water is 100oC, we have to understand why a liquid boils. By definition, a liquid boils when the vapor pressure of the gas escaping from the liquid is equal to the pressure exerted on the liquid by its surroundings, as shown in the figure below.
The normal boiling point of water is 100oC because this is the temperature at which the vapor pressure of water is 760 mmHg, or 1 atm. Under normal conditions, when the pressure of the atmosphere is approximately 760 mmHg, water boils at 100oC. At 10,000 feet above sea level, the pressure of the atmosphere is only 526 mmHg. At these elevations, water boils when its vapor pressure is 526 mmHg, which occurs at a temperature of 90oC.
Liquids often boil in an uneven fashion, or bump. They tend to bump when there aren’t any scratches on the walls of the container where bubbles can form. Bumping is easily prevented by adding a few boiling chips to the liquid, which provide a rough surface upon which bubbles can form. When boiling chips are used, essentially all of the bubbles that rise through the solution form on the surface of these chips.
Difference between Boiling and Evaporation
| Evaporation | Boiling |
| It occurs at all temperature | It occurs at the boiling point of the liquid |
| It causes cooling | It does not cause cooling |
| It occurs only at the surface | It occurs in every part of the liquid |
| It is not affected by the mass of the liquid exposed | It is affected by the mass of the liquid exposed |
| It does not depend on the container of the liquid | It depends on the container, because they absorb their own energy first |
| Wind assists evaporation | Wind has no effect on boiling |
Effects of Impurities on Boiling
Impurities affect the boiling point of a liquid, because their presence increases the boiling point of the liquid, compared to the boiling point of a pure solvent.
Effect of Pressure on Boiling
Pressure affects the boiling point of a liquid, because an increase in pressure will lead to a decrease in boiling point. This explanation has a practical application in pressure cooker which is a sauce-pan with lid that can be held be down.
Application of Pressure on Boiling Point
1. It is used in the principle of pressure cooker
2. The aircraft flying at high altitude, where air is of lower pressure than normal, needs to be pressurized so that the people can be at their normal pressure.
3. Astronauts must wear space suits not only for breathing but for them to be at right pressure.
Sublimation
This is a process by which a solid is heated straight to vapour without passing through the intermediate liquid state. The solid molecules acquire some kinetic energy which is very great and instead of the solid melting into a liquid phase, it is converted into gaseous or vapour state at a very high temperature, e.g. dry ice when changed to vapour.
Effect of Pressure on Melting Point
The increase in pressure on a substance lowers it melting point. Consider an ice placed on a insulator and a thin wire with heavy weight attached to both ends and hung over the block., after sometime, it is observed that the wire starts passing through the ice, but the block remains solid behind it and the water above the wire passes through the ice block and the block does not slip. As the wire passes through the ice, the pressure above it decreases, thus raising the freezing point of melted ice above it when freezes again. This process is called regelation.
Effect of Impurities on Melting Point
When there are impurities, e.g. salt, sand, etc in a substance, this lowers the melting point. For example, when a salt is mixed with ice, the ice melts taking heat from the salt and freezes at a temperature below 0oC – 23oC, from normal freezing point of ice. The mixture is also called freezing mixture.
Application of Pressure and Impurities
(i) In temperature climate, the sea which is made of salt will not freeze even when it is covered with ice. This explains how the aquatic animals adapt to it.
(ii) Salt thrown on the road full of ice brings down the freezing point and the melting point of the ice, so as to become droplet of water.
Questions
1. Molecules with high speed near the surface of the liquid may have enough …………………. to break away from the attraction of other molecules and move outside the liquid surface as molecules of vapour.
A. Potential Energy B. Kinetic Energy C. Mechanical Energy D. Electrical Energy
2. Which of these is not correct about Boiling Point?
A. It is affected by the mass of the liquid exposed B. It does not cause cooling C. It does not depend on the container of the liquid D. Wind has no effect on it.
3. Which of these is not correct about Evaporation?
A. It does not cause cooling
B. It occurs at all temperature
C. It does not depend on the container of the liquid
D. It is not affected by the mass of the liquid exposed.
4. The boiling point of water is at
A. 100°C B. 90oC C. 75oC D. 120oC
5. The boiling point of Mercury is at
A. 345oC B 357°C C. 405oC D 250oC
Answers
1. B 2. C 3. A 4. A 5. B
VAPOUR PRESSURE
Physics SS 2 Week 6
Topic: VAPOUR PRESSURE
INTRODUCTION
Vapour pressure– pressure exerted by a vapour when the vapour is in equilibrium with the liquid or solid form, or both, of the same substance – i.e., when conditions are such that the substance can exist in both or in all three phases. Vapour pressure is a measure of the tendency of a material to change into the gaseous or vapour state, and it increases with temperature. The temperature at which the vapour pressure at the surface of a liquid becomes equal to the pressure exerted by the surroundings is called the boiling point of the liquid.
Saturated Vapour Pressure
The process of evaporation in a closed container will proceed until there are as many molecules returning to the liquid as there are escaping. At this point the vapor is said to be saturated, and the pressure of that vapor (usually expressed in mmHg) is called the saturated vapor pressure.
| Since the molecular kinetic energy is greater at higher temperature, more molecules can escape the surface and the saturated vapor pressure is correspondingly higher. If the liquid is open to the air, then the vapor pressure is seen as a partial pressure along with the other constituents of the air. The temperature at which the vapor pressure is equal to the atmospheric pressure is called the boiling point |
Vapour Pressure Relation to boiling point of liquids
As a general trend, vapor pressures of liquids at ambient temperatures increase with decreasing boiling points. This is illustrated in the vapor pressure chart that shows graphs of the vapor pressures versus temperatures for a variety of liquids.
For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−24.2 °C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure.
Although the relation between vapor pressure and temperature is non-linear, the chart uses a logarithmic vertical axis to produce slightly curved lines, so one chart can graph many liquids. A nearly straight line is obtained when the logarithm of the vapor pressure is plotted against 1/(T+230) where T is the temperature in degrees Celsius. The vapor pressure of a liquid at its boiling point equals the pressure of its surrounding environment
Saturated and Unsaturated Vapour
Saturated vapour is one in which the vapour is in a state of dynamic equilibrium with its own liquid in a closed space.
Consider a tube immersed upside down in a bath of mercury. The mercury which is concave to glass rises through the tube, leaving the empty space above it. This vapour which is in contact with its own liquid in space is called saturated vapour while the pressure exerted by the saturated vapour is called saturated vapour pressure. The saturated pressure varies with temperature and does not obey the gas law.
The saturated vapour pressure of water is equal to the external pressure at which water boils approximately and it is 760mmHg at 100oC for pure water. This enables the boiling point of a liquid to be defined as the temperature at which the saturated vapour pressure becomes equal to the external atmospheric pressure.
During evaporation, the number of molecules leaving and returning to the liquid is equal and this is best explained by the kinetic theory’s explanation of saturated vapour.
Measurement of Saturated Vapour Pressure
In the diagram below a small amount of liquid introduced at the top of the mercury column results in the column dropping from 760 mm to 630 mm. The saturated vapour pressure of the liquid is 130 mm.
Unsaturated Vapour
Unsaturated vapour is one in which the vapour is not in contact with its own liquid in a closed space.
Here, the vapour is not in equilibrium with its liquid. The pressure is less than the s.v.p and at higher temperature.
During evaporation, the number of molecules leaving is greater than the number of those returning to the liquid and this is best explained by the kinetic theory explanation of unsaturated vapour.
Differences between a Saturated and an Unsaturated Vapour
| Saturated Vapour | Unsaturated Vapour |
| Saturated vapour is in contact with its own liquid. | Unsaturated vapour is not in contact with its liquid. |
| The pressure of a saturated vapour is independent of its volume. | The pressure of an unsaturated vapour is approximately inversely proportional to its volume. |
Similarities
1. Both are directly proportional to its absolute temperature.
Properties of Saturated Vapour Pressure
I. The saturated vapour pressure increases with a rise in temperature and decrease with a fall in temperature.
II. The saturated pressure of a liquid does not depend on the surface occupied by the vapour
III. The saturated vapour pressure depends on the nature of the substance.
IV. The total pressure exerted by the vapours of all substances is equal to the sum of the pressures exerted by the vapour of individual substances, i.e.,
PT = P1 + P2 + P3 + …………………….. + Pn
V. The saturated vapour pressure of a liquid is independent of the pressure of the vapour of other liquid
VI. The vapour must not have any chemical action.
Humidity
Humidity of the air refers to the amount of water vapour present in the air. If the air in an environment is dry, the sweat from our body evaporates faster than when the air is damp and made up of water vapour. We describe a moist air as humid air.
Relative Humidity
The amount of water vapor in the air at any given time is usually less than that required to saturate the air. The relative humidity is the percent of saturation humidity, generally calculated in relation to saturated vapor density.
Relative humidity is the amount of moisture in the air compared to what the air can “hold” at that temperature. When the air can’t “hold” all the moisture, then it condenses as dew.
Relative humidity is the term used to describe the humidity of the air. It is defined as the ratio of the mass of vapour actually present in a certain volume of air, at a room tempertaure to the mass of water vapour required to saturate the same volume of air at the same temperature.
Relative humidity can be mathematically represented as
Relative humidity = m/M x 100%
Since the mass of the water in a given volume is roughly proportional to its pressure, the relative humigity is also given by the ratio:
S.V.P at dew point/S.V.P at air temperature x 100%
The relative humidity is usually expressed in %. Relative humidity of air can be measured using hygrometer. Example of hygrometer are
(i) Regnault’s hygrometer
(ii) Daniel’s hygrometer
(iii) Wet & dry hygrometer
(iv) Dew point bulb hygrometer
The commonly used hygrometer is the wet and dry hygrometer.
Dew Point
Dew point is the temperature at which the water vapour present in the atmosphere is just sufficient to saturate. This means that the actual vapour pressure at a room temperature is equal to the saturated vapour pressure at a dew point. Dew point can be measured using the dew point hygrometer can also be used to find the humidity of the air.
If the temperature falls below the dew point, condensation will form.
If the temperature stays above the dew point, condensation will not form.
Air consists in part of water vapour. The amount of water vapour present in the air varies, depending on temperature, the amount of evaporation from surface water, whether or not it has rained… The air can only hold so much water. The amount of water the air can hold depends on temperature.
In general the temperature increases by day and decreases by night. Water evaporates during the day, when the temperature is above the dew point and the air can absorb the water, and falls during the night. If the temperature falls below the dew point, condensation will form. Dew is common – in the desert some animals get most or all of the water they need from dew.
Dew can be a very localized phenomenon. A person entering a warm room from the cold outside may have condensation form on their glasses. Because their glasses are cold, they will lower the temperature in the region of their glasses, maybe below the dew point, in which case condensation will form.
Every liquid has a dew point for a specific pressure of vapour. The phenomenon has a wide range of uses:
To determine the humidity of the air – how much water it holds. The temperature is lowered until condensation begins to form. The temperature at which this happens is the dew point. The humidity can then be determined.
To extract substances from the air. The air is a mixture of substances, all with differing dew points. We can extract them all one by one by cooling the air. As the temperature passes each dew point, the corresponding substance will condense.
Question
1. Vapour pressure ispressure exerted by a vapour when the vapour is ……………….. with the liquid or solid form, or both, of the same substance.
A. Lower B. In equilibrium C. Higher D. at variance
2. Vapor pressures of liquids at ambient temperatures ………………………………………… boiling points.
A. Increase with decreasing B. decrease with increasing C. Increase with increasing D. decrease with decreasing.
3. Vapour pressure is a measure of the tendency of a material to change into the …………………………….. state, and it increases with temperature.
A. gaseous or solid B. gaseous or vapour C. solid or liquid D. liquid or gaseous
4. Which of this is not correct about Relative Humidity?
A. The amount of water vapor in the air at any given time is usually less than that required to saturate the air.
B. The relative humidity is the percent of saturation humidity, generally calculated in relation to saturated vapor density.
C. Relative humidity can be mathematically represented as ‘Relative humidity = m/M x 100%’
D. Relative humidity is the term used to describe the humidity of the moisture.
5. To determine the humidity of the air – how much water it holds. The temperature is ……………………….. until condensation begins to form.
A. Made higher B. Made higher C. lowered D. Extinct from existence
Answers
1. B 2. A 3. B 4. D 5. C
LATENT HEAT
Physics SS 2 Week 5
Topic: LATENT HEAT – FUSION, VAPORIZATIONS AND VERIFICATION
INTRODUCTION
Any substance will undergo a change in the temperature if the energy is transferred between the substance and its environment. In some instances the transfer of energy does not result in a change in temperature and can occur or take place when the physical characteristics of the substance change from one form to another or undergo phase change.
If there is a phase change due to the change in the internal energy but no overall temperature change then we are definitely dealing with Hidden Heat or Latent Heat.
When energy is transferred to a substance, usually, temperature of the substance increases. If the substance is at higher temperature then the surroundings, temperature of the substance decreases, as heat is transferred from the system or substance to the surroundings. From this we can conclude that a substance undergoes change in temperature whenever flow of energy transfer between system and its surroundings takes place.
But there are scenarios during which energy transfer between system and its surroundings does not result in the change in temperature of the system. This occurs whenever system changes from one of its phase to another or we can say that when the transfer of energy results in the change in the physical properties of the system. This change is termed as Phase Change or Phase Transition. Two main Phase transitions are,
1. Solid to Liquid
2. Liquid to Gas
Other phase transition is when change takes place in the crystalline structure of the solid. When phase Transition occurs temperature of the system does not change but change in the internal energy of the system takes place.
At the boiling point of the water when heat is transferred to the water it results in the breaking of molecular bonds in water. As a result, the molecules become apart as their potential and kinetic energies get increased and water gets converted to the gaseous state. Every substance has different molecular and atomic structure. So, for the phase transition to occur every substance requires different amount of energy depending on their internal structure. It also depends on the mass of substance involved for the phase transition. The substance of a particular type with larger quantity and mass requires more heat for phase transition as compared to the other. It takes less energy to boil water in cooking pan than to boil a lake.
If a Q amount of energy needs to be transferred for phase change of a substance having mass m, the ratio symbolizes an important property of that substance. As the energy added or removed is not resulting in the change of temperature, the quantity L is termed as the latent heat. It can also be termed as the hidden heat of the substance.
Latent heat for a substance depends mainly on two factors:
1. Phase change Nature
2. Properties (atomic, molecular structure of the substance)
Latent Heat Formula
From the definition, it is clear that the amount of heat required for a phase transition is latent heat. The mathematical representation of the given statement is,
Q = mL
L = Qm
Where,
L = Latent heat of the substance
Q = Amount of energy transferred for the Phase change
m = Mass of the substance
Latent Heat of Vaporization
Latent heat of Vaporization is the Latent heat (explained above) when phase of the substance changes from Liquid to gaseous state. Latent heat of vaporization is denoted by LV.
Definition of the specific latent heat of vaporization
The specific latent heat of vaporization of a substance is the quantity of heat required to change unit mass of the substance from the liquid to the vapour state without change of temperature. (Symbol = L ).
The SI unit of specific latent heat of vaporization is the Joule per kilogram (J / kg). However, in order to avoid having to write every large numbers the alternative units Kj / kg or MJ / kg may be used instead.
1 Kj = 1000 j
1 Mj = 100000 j
So we may express the specific latent heat of vaporization of water as 2260 Kj / kg or 2.26 Mj / kg. The old thermal unit was calorie per gram (cal / g)).
Latent Heat of Fusion
Latent Heat of Fusion is the latent heat (explained above) when phase of the substance changes from Solid to Liquid phase. Latent heat of Fusion is denoted by LF. Also fuse means melting.
Just as latent heat is taken in when water changes to vapour at the same temperature, so the same thing occurs when ice melts to form water. But in this case the latent heat is not so great. It requires only 336000 j to convert 1 kg of ice at 0 °C to water at the same temperature. Likewise, when water at 0°C freezes into ice, the same quantity of heat is given out for every 1 kg of ice formed. This is called the specific latent heat of ice.
As already mentioned, the phenomenon of latent heat is not confined to water alone. Other substances also absorb latent heat when they melt; conversely, they give out latent heat on solidifying. This heat is called latent heat of fusion.
Latent Heat of Substances
Latent Heat of Water, Latent Heat of Ice and Latent Heat of Steam are given in the tables below. Latent Heat of Fusion and Latent Heat of Vaporization for different substances are given in the below tables.
| Substance | Melting Point (°C) | Latent Heat Of Fusion (J/kg) | Boiling Point (°C) | Latent heat Of Vaporization (J\kg) |
| Helium | -269.65 | 5.23×103 | -268.93 | 2.09×104 |
| Nitrogen | -209.97 | 2.55 ×104 | -195.81 | 2.01×105 |
| Oxygen | -218.79 | 1.38 ×104 | -182.97 | 2.13×105 |
| Ethyl Alcohol | -114 | 1.04 ×105 | 78 | 8.54 ×105 |
| Water | 0.00 | 3.33 ×105 | 100.00 | 2.26×106 |
| Sulphur | 119 | 3.81 ×104 | 444.60 | 3.26×105 |
| Lead | 327.3 | 2.45 ×104 | 1750 | 8.70×105 |
| Aluminum | 660 | 3.97 ×105 | 2450 | 1.14×107 |
| Silver | 960.80 | 8.82 ×104 | 2193 | 2.33×106 |
| Gold | 1063.00 | 6.44 ×104 | 2660 | 1.58×106 |
| Copper | 1083 | 1.34 ×105 | 1187 | 5.06×106 |
Questions
1. If the specific latent heat of vaporization for water is 2.25 kJ/g, then the amount of heat required to vaporize 4 g of boiling water to steam at 100oC is
A. 9 J B. 90 J C. 900 J D. 9000 J
2. The heat gained or lost by a body during a change of state is the product of its _______ and the specific latent heat.
A. Weight B. Volume C. Mass D. Breadth
3. Vaporization point and _______ have the same numerical value
A. Fusion point B. Solidification point C. melting point D. liquefaction point
4. If 1625 J of energy are expended to rub two ice blocks against each other and the specific latent heat of ice is 325 J/g, then the mass of the melted ice is
A. 5 g B. 10 g C. 15 g D. 20 g
5. The fixed temperature at which a gas changes into its liquid state is called the _______.
A. Fusion Point B. Solidification Point C. Vaporization Point D. liquefaction point
Answer
1. D 2. C 3. D 4. A 5. D
GAS LAWS
Physics SS 2 Week 7
Topic: GAS LAWS
INTRODUCTION
The early gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.
Boyle’s Law
Boyle’s law shows that, at constant temperature, the product of an ideal gas’s pressure and volume is always constant. It was published in 1662. It can be determined experimentally using a pressure gauge and a variable volume container. It can also be found through the use of logic; if a container, with a fixed number of molecules inside, is reduced in volume, more molecules will hit the sides of the container per unit time, causing a greater pressure.
As a mathematical equation, Boyle’s law is:
P1V1 = P2V2
where P is the pressure (Pa), V the volume (m3) of a gas, and k1 (measured in joules) is the constant from this equation—it is not the same as the constants from the other equations below.
This is known as Boyle’s law which states: the volume of a given mass of gas is inversely proportional to its pressure, if the temperature remains constant. Mathematically this is:
V = k/P
where k is a constant (NOT Boltzmann’s constant or Coulomb’s constant).
Charles’s Law, or the law of volumes, was found in 1787 by Jacques Charles. It says that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature.
V1/T1 = V2/T2
Gay-Lussac’s law, or the pressure law, was found by Joseph Louis Gay-Lussac in 1809. It states that the pressure exerted on the sides of a container by an ideal gas of fixed volume is proportional to its temperature.
P1/T1 = P2/T2
Avogadro’s law states that the volume occupied by an ideal gas is proportional to the number of molespresent in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or litres). The relation is given by
V1 / n1 = V2 / n2
where n is equal to the number of moles of gas (the number of molecules divided by Avogadro’s Number).
The combined gas lawor general gas equation is formed by the combination of the three laws, and shows the relationship between the pressure, volume, and temperature for a fixed mass of gas:
PV = K5T
This can also be written as:
P1V1/T1 = P2V2/T2
With the addition of Avogadro’s law, the combined gas law develops into the ideal gas law:
PV = nRT
where
P is pressure
V is volume
n is the number of moles
R is the universal gas constant
T is temperature (K)
where the constant, now named R, is the gas constant with a value of .08206 (atm∙L)/(mol∙K). An equivalent formulation of this law is:
PV = kNT
where
P is the absolute pressure
V is the volume
N is the number of gas molecules
k is the Boltzmann constant (1.381×10−23 J·K−1 in SI units)
T is the temperature (K)
These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.
This law has the following important consequences:
1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.
Other Gas Laws
Graham’s law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro’s law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.
Dalton’s law of partial pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton’s Law is as follows:
Ptotal = P1 + P2 + P3 + … + Pn
OR
Ptotal = Pgas + PH2O
where PTotal is the total pressure of the atmosphere, PGas is the pressure of the gas mixture in the atmosphere, and PH2O is the water pressure at that temperature.
Henry’s law states that:
At constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to thepartial pressure of that gas in equilibrium with that liquid.
Questions:
A mass of gas at 70C and 70cm of mercury has a volume of 1000 cm3. Determine its volume at 270C and pressure of 85 cm of mercury.
A. 788.35 cm3 B. 782.35 cm3 C. 882.35 cm3 D. 805.54 cm3
2. A vessel is filled with a gas at a temperature 300C and a pressure of 76 cm Hg. Calculate the final pressure if the volume of the gas is doubled while it is heated to 800C.
A. 55.56 cm Hg B. 23.44 cm Hg C. 44.27 cm Hg D. 34.57 cm Hg
3. A fixed mass of gas is heated at constant pressure from 100C to 900C. If its volume at 100C is 200 cm2, calculate the volume at 900.
A. 256.54 cm3 B. 735.56 cm3 C. 345.24 cm3 D. 400.45 cm3
4. The pressure of a gas at constant volume is 90 cm Hg at 200C. Calculate its pressure at 700C.
A. 205.90 cm Hg B. 105.3 cm Hg C. 45.24 cm Hg D. 237.6 cm Hg
5. In this equation PV = nRT, what does n stands for?
A. number of base B. number of moles C. universal gas constant D. temperature constant
Answers
1. C 2. C 3. A 4. B 5. B
PRODUCTION AND PROPAGATION OF WAVES
Physics SS 2 Week 8
Topic: PRODUCTION AND PROPAGATION OF WAVES
WHAT IS A WAVE?
A wave is a disturbance which travels through a medium transferring energy from one point to another without causing any permanent displacement of the medium.
Not all waves, however, requires a material for their propagation.
Mechanical waves are those waves that require a material a material medium for their propagation. Examples of such waves are water waves, sound waves, waves on a rope or string.
Electromagnetic waves are waves that do not require a material medium for propagation.
Examples are light waves, radio waves, X-rays and gamma-rays.
The Ripple Tank
The ripple tank is a container that when filled with water permits the study of water waves. A concentrated light source positioned above the tank forms images of the waves on a screen beneath the tank. Wave crests and troughs project light and dark lines in the screen.
The crests act as converging lenses that focus light, producing the bright lines..The troughs act as diverging lenses that scatter light, producing the dark lines.
The depth at which the dipper is placed affects the amplitude of the waves, while the frequency of waves is determined by frequency of vibration of the dipper.
Refraction of waves and the depth of ripple tank
Refraction of waves involve a change in the direction of waves as they pass from one medium to another. Refraction is the bending of the path of the waves. It is accompanied by a change in speed and wavelength of the waves. It was mentioned that the speed of a wave is dependent upon the properties of the medium through which the waves travel. So if the medium (and its properties) are changed, the speed of the waves are changed.
The most significant property of water which would affect the speed of waves traveling on its surface is the depth of the water.
This boundary behavior of water waves can be observed in a ripple tank if the tank is partitioned into a deep and a shallow section. If a pane of glass is placed in the bottom of the tank, one part of the tank will be deep and the other part of the tank will be shallow. Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wave fronts get closer together), and slow down (they take a longer time to travel the same distance). When traveling from deep water to shallow water, the waves are seen to bend in such a manner that they seem to be traveling more perpendicular to the surface. If traveling from shallow water to deep water, the waves bend in the opposite direction.
Water waves travel fastest when the medium is the deepest. Thus, if water waves are passing from deep water into shallow water, they will slow down and also the wavelength of the plane waves shorten. The frequency remains the same as it is determined by the dipper. Using the equation, v:f x L, the speed of the waves is therefore slower at the shallow water.
Three types of waves
Mechanical waves require a material medium to travel (air, water, ropes). These waves are divided into three different types.
Transverse waves cause the medium to move perpendicular to the direction of the wave. For example, a string wave propagates horizontally through space while the string itself (the wave’s medium) moves up and down. Transverse waves are characterized by their frequency (number of wave crests per second), amplitude (height of a wave crest) and wavelength (distance between two crests). Seismic waves are also transverse waves.
Longitudinal waves cause the medium to move parallel to the direction of the wave. A sound wave is a classic example of such a wave. When you sound a tuning fork, for example, the vibration of its prongs causes nearby molecules in the air to vibrate back and forth horizontally. This displaces nearby particles, causing a domino-effect that propagates the wave through space. You can make a visible longitudinal wave by holding a slinky between your hands and moving one hand side to side, causing the slinky to expand and contract horizontally.
Surface waves are both transverse waves and longitudinal waves mixed in one medium.
Electromagnetic waves do not require a medium to travel (light, radio). Electromagnetic waves, on the other hand, can travel through the vacuum of space. Light, for example, travels 93 million miles from the Sun to Earth without requiring a vibrating medium in between. Matter waves are produced by electrons and particles.
General Wave Equation
a wave is produced when a vibrating source periodically disturbs the first particle of a medium. This creates a wave pattern that begins to travel along the medium from particle to particle. The frequency at which each individual particle vibrates is equal to the frequency at which the source vibrates. Similarly, the period of vibration of each individual particle in the medium is equal to the period of vibration of the source. In one period, the source is able to displace the first particle upwards from rest, back to rest, downwards from rest, and finally back to rest. This complete back-and-forth movement constitutes one complete wave cycle.
The diagrams show several “snapshots” of the production of a wave within a rope. The motion of the disturbance along the medium after every one-fourth of a period is depicted. Observe that in the time it takes from the first to the last snapshot, the hand has made one complete back-and-forth motion. A period has elapsed. Observe that during this same amount of time, the leading edge of the disturbance has moved a distance equal to one complete wavelength. So in a time of one period, the wave has moved a distance of one wavelength. Combining this information with the equation for speed (speed = distance/time), it can be said that the speed of a wave is also the wavelength/period.
Speed = Wavelength/Period
Since the period is the reciprocal of the frequency, the expression 1/f can be substituted into the above equation for period. Rearranging the equation yields a new equation of the form:
Speed = Wavelength x Frequency
V = f x λ
As a test of your understanding of the wave equation and its mathematical use in analyzing wave motion, consider the following three-part question:
Questions
Stan and Anna are conducting a slinky experiment. They are studying the possible effect of several variables upon the speed of a wave in a slinky. Their data table is shown below. Fill in the blanks in the table, analyze the data, and answer the following questions.
1. Medium Wavelength Frequency
Zinc 1.75 m 2.0 Hz
A. 3.5 m/s B. 4.5 m/s C. 6.5 m/s D. 8 m/s
2. Medium Wavelength Frequency
Copper 1.19 m 2.1 Hz
A. 4.5 m/s B. 2.9 m/s C. 2.5 m/s D. 6.5 m/s
3. As the wavelength of a wave in a uniform medium increases, its frequency will ………………………………
A. decrease B. increase C. remain the same D. be zero
4. The speed of a wave depends upon (i.e., is causally affected by) …
A. the properties of the medium through which the wave travels B. the wavelength of the wave C. the frequency of the wave D. both the wavelength and the frequency of the wave
5. Dawn and Aram have stretched a slinky between them and begin experimenting with waves. As the frequency of the waves is doubled,
A. the wavelength is halved and the speed remains constant B. the wavelength remains constant and the speed is double C. both the wavelength and the speed are halved D. both the wavelength and the speed remain constant.
Answers
1. A 2. C 3. C 4. A 5. A
PROPERTIES OF WAVES
Physics SS 2 Week 9
Topic: PROPERTIES OF WAVES
INTRODUCTION
A wave is a transfer of energy from one point to another without the transfer of material between the two points.
It is important to realize that a wave is quite a different object than a particle. A baseball thrown through a window transfers energy from one point to another, but this involves the movement of a material object between two points. A common example of a wave is a wave on the ocean – we know they carry energy, as they cause erosion on the shore, but material (i. e. , water) is not continuously being transferred onto the shore. Another example of a wave is a sound wave, which is vibrations of air molecules which propagate from one place to another. These also carry energy, but do not involve the mass movement of air from one place to another.
A simple type of wave is illustrated below.
Reflection of Waves
If a linear object attached to an oscillator bobs back and forth within the water, it becomes a source of straight waves. These straight waves have alternating crests and troughs. As viewed on the sheet of paper below the tank, the crests are the dark lines stretching across the paper and the troughs are the bright lines.
These waves will travel through the water until they encounter an obstacle – such as the wall of the tank or an object placed within the water. The diagram at the right depicts a series of straight waves approaching a long barrier extending at an angle across the tank of water. The direction that these wavefronts (straight-line crests) are traveling through the water is represented by the blue arrow. The blue arrow is called a ray and is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the water, these waves bounce off the water and head in a different direction. The diagram below shows the reflected wavefronts and the reflected ray. Regardless of the angle at which the wavefronts approach the barrier, one general law of reflection holds true: the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. This is known as the law of reflection.
The discussion above pertains to the reflection of waves off of straight surfaces. But what if the surface is curved, perhaps in the shape of a parabola? What generalizations can be made for the reflection of water waves off parabolic surfaces? Suppose that a rubber tube having the shape of a parabola is placed within the water. The diagram at the right depicts such a parabolic barrier in the ripple tank. Several wavefronts are approaching the barrier; the ray is drawn for these wavefronts. Upon reflection off the parabolic barrier, the water waves will change direction and head towards a point. This is depicted in the diagram below. It is as though all the energy being carried by the water waves is converged at a single point – the point is known as the focal point. After passing through the focal point, the waves spread out through the water.
Refraction of Waves
Reflection involves a change in direction of waves when they bounce off a barrier. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves. In Lesson 2, it was mentioned that the speed of a wave is dependent upon the properties of the medium through which the waves travel. So if the medium (and its properties) is changed, the speed of the waves is changed. The most significant property of water that would affect the speed of waves traveling on its surface is the depth of the water. Water waves travel fastest when the medium is the deepest. Thus, if water waves are passing from deep water into shallow water, they will slow down, this decrease in speed will also be accompanied by a decrease in wavelength. So as water waves are transmitted from deep water into shallow water, the speed decreases, the wavelength decreases, and the direction changes.
This boundary behavior of water waves can be observed in a ripple tank if the tank is partitioned into a deep and a shallow section. If a pane of glass is placed in the bottom of the tank, one part of the tank will be deep and the other part of the tank will be shallow. Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance). When traveling from deep water to shallow water, the waves are seen to bend in such a manner that they seem to be traveling more perpendicular to the surface. If traveling from shallow water to deep water, the waves bend in the opposite direction.
Diffraction of Waves
Reflection involves a change in direction of waves when they bounce off a barrier; refraction of waves involves a change in the direction of waves as they pass from one medium to another; and diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path. Water waves have the ability to travel around corners, around obstacles and through openings.
This ability is most obvious for water waves with longer wavelengths. Diffraction can be demonstrated by placing small barriers and obstacles in a ripple tank and observing the path of the water waves as they encounter the obstacles. The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. In fact, when the wavelength of the waves is smaller than the obstacle, no noticeable diffraction occurs.
Diffraction of water waves is observed in a harbor as waves bend around small boats and are found to disturb the water behind them. The same waves however are unable to diffract around larger boats since their wavelength is smaller than the boat. Diffraction of sound waves is commonly observed; we notice sound diffracting around corners, allowing us to hear others who are speaking to us from adjacent rooms. Many forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound waves. Owls for instance are able to communicate across long distances due to the fact that their long-wavelength hoots are able to diffract around forest trees and carry farther than the short-wavelength tweets of songbirds. Diffraction is observed of light waves but only when the waves encounter obstacles with extremely small wavelengths (such as particles suspended in our atmosphere).
Reflection, refraction and diffraction are all boundary behaviors of waves associated with the bending of the path of a wave. The bending of the path is an observable behavior when the medium is a two- or three-dimensional medium. Reflection occurs when there is a bouncing off of a barrier. Reflection of waves off straight barriers follows the law of reflection. Reflection of waves off parabolic barriers results in the convergence of the waves at a focal point. Refraction is the change in direction of waves which occurs when waves travel from one medium to another. Refraction is always accompanied by a wavelength and speed change. Diffraction is the bending of waves around obstacles and openings. The amount of diffraction increases with increasing wavelength.
Interference
Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let’s suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units. The diagrams below depict the before and during interference snapshots of the medium for two such pulses. The individual sine pulses are drawn in red and blue and the resulting displacement of the medium is drawn in green.
Polarization is a property of waves that can oscillate with more than one orientation. Electromagnetic waves, such as light, and gravitational waves exhibit polarization whereas this is not a concern with sound waves in a gas or liquid which have only one possible polarization, namely the direction in which the wave is travelling.
In an electromagnetic wave such as light, both the electric field and magnetic field are oscillating but in different directions; by convention the “polarization” of light refers to the polarization of the electric field. Light which can be approximated as a plane wave in free space or in an isotropic medium propagates as a transverse wave—both the electric and magnetic fields are perpendicular to the wave’s direction of travel. The oscillation of these fields may be in a single direction (linear polarization), or the field may rotate at the optical frequency (circular or elliptical polarization). In that case the direction of the fields’ rotation, and thus the specified polarization, may be either clockwise or counter clockwise; this is referred to as the wave’s chirality or handedness.
The most common optical materials (such as glass) are isotropic and simply preserve the polarization of a wave but do not differentiate between polarization states. However there are important classes of materials classified as birefringent or optically active in which this is not the case and a wave’s polarization will generally be modified or will affect propagation through it. A polarizer is an optical filter that transmits only one polarization.
ASSESSMENT
- Which of following is not a longitudinal wave?
(a) Ultrasonic wave
(b) Infrasonic wave
(c) Infrared wave
(d) Seismic wave - If wavelength of a wave moving on a slinky spring with a frequency of 5 Hz is equal to 0.5 m then speed of wave is equal to
(a) 0.1 m s-1
(b) 2.5 m s-1
(c) 10 m s-1
(d) None of above - For a constant frequency, wavelength of an electromagnetic wave is
(a) directly proportional to its velocity
(b) inversely proportional to its velocity
(c) independent of its velocity
(d) None of above - All waves can be classified into two categories which are
(a) Sound waves and electromagnetic waves
(b) Transverse waves and electromagnetic waves
(c) Longitudinal waves and electromagnetic waves
(d) Transverse waves and longitudinal waves - If amplitude of a wave is denoted as ‘A’, then vertical displacement between a crest and a trough of a wave in terms of ‘A’ would be
(a) 1 ⁄ 2 of A
(b) A
(c) 2A
(d) None of above
ANSWERS
- c
- b
- a
- d
- c
LIGHT WAVES
Physics SS 2 Week 10
Topic: LIGHT WAVES
Sources
Light is a form of energy, called luminous energy. This energy causes a sensation of vision, enabling us to see. There are various sources of light, for example the sun and the stars are natural sources of light. Artificial sources of light are the candle, electric torch and electric lamp, incandescent and arc lights and fluorescent light.
Self luminous or luminous sources of light are those that generate and emit light by themselves. Examples are the sun, star, fire-flies and some deep sea fishes and the artificial light sources to illuminate them. They are seen only when they illuminate light from their luminous body. For example, light from a car headlamp falling on a road sign in the night, causes the sign to throw back part of this light into the eyes of the car-driver thereby enabling the road sign to be seen. The road sign is a non-luminous body, the headlamp is a luminous body, an artificial luminous body. Examples of non-luminous bodies are a page of a book, a person’s face, a brick and the moon. The sun’s rays illuminate the moon and make it to appear luminous in the night.
Transmission of Light
Light is an electromagnetic wave. It can pass through a vacuum and through a material medium. If light shines on a body, part of the light is transmitted through the body, the rest is reflected. The amount of light passing through a body is depends on the nature of the body. If a light percentage of light falling on a body passes through it, the body is said to be transparent. Examples of transparent bodies are glass and water. Because light is easily transmitted through these transparent bodies, we can see objects through them easily. Some objects like frosted glass and tissue paper allow some small amount to pass through them. Such objects are called translucent objects. Because the amount of light passing through translucent bodies is small, objects cannot be seen clearly through them. Some other bodies do not allow any light to pass through them. These are called opaque objects. Examples of opaque objects are wood, bricks, walls and metal sheets.
Rays and Beams of Light
A light ray is the direction or path along which light energy flows. Such rays are indicated in diagrams by thin lines in arrow head which indicate the direction of travel of the light. A collection of rays is called a beam. There are three types of beams.
(i) A parallel is one in which the light rays are parallel to one another. Search-lights give off parallel beams of light.
(ii) A convergent beam is one which the rays converge or meet at a point. A hand lens can be used to produce such a beam.
(iii) A divergent beam is one in which the light rays all come from a point and spread out or diverge from the source. Lamps produce a divergent beam of light.
The Ray Box
Rays of light are produced in the laboratory by means of a ray box. A simple laboratory ray box consists of a box made of wood or cardboard inside which is a source of light, e.g., a candle or an electric lamp
Reflection in Plane and Curved Mirrors
Mirrors are the contrivances that reflect light waves. They are broadly classified as plane mirrors and curved mirrors. Curved mirrors, as the name suggests, have curved surfaces that reflect the light rays. Basically these curved surfaces are parts of spherical surfaces and hence they are also called as spherical mirrors. The reflecting surface may be bulged towards the object or concave right to the object. Curved mirrors have extensive uses in various applications.
Convex Mirror
A mirror with a spherical surface and reflecting from the exterior the curvature is called a convex mirror. A convex mirror is also known as Diverging Mirror as it diverges the incident rays after reflection.
The mirror is defined as an optical device which has the capacity to reflect beam of light and form a clear identical image. Some beams are filtered through mirrors while some are reflected from it. But they preserve only colour or diffused light. Mirrors are used for decoration, to see our clear image, for scientific purpose, in apparatus like cameras, telescope, machines etc. generally mirrors are made up for visible light. Some common types of mirrors are flat surface mirrors and curved surface mirrors.
The plane mirrors are flat surface mirrors while the curved surface mirrors are produced a clear image with focusing of light. The spherical mirrors are of two types that are concave and convex mirrors. These are used because of their one of the main advantage that they form an image without chromatic aberration. Here we are discussing about the convex spherical mirrors, their image formation process, and some different types of convex mirrors.
Concave Mirror
A mirror with a spherical surface and reflecting from the interior of the curvature is called a concave mirror. A concave mirror is also known as Converging Mirror as it converges the incident rays after reflection.
As mentioned, the normal to a spherical surface is always towards the center. Hence in cases where the inner surface of curved mirror is reflecting, the angle of reflection falls towards the object. Therefore, the rays which fall on the surface of a mirror concave opposite to the object are converged.
For understanding the concept of the mirror, we should know about the law of reflection which states that when a beam of light is passed through a surface then it is deflected at some angle. This angle is the angle of reflection while the incoming angle is the angle of incidence. Both are equal. A beam of light which passes through the space is invisible. It can be seen only when it hits something through which it is scattered. Light is not scattered by mirrors.
Curved mirrors can reflect the light due to their curved surface while the plane mirrors cannot. The flat mirror makes virtual image while the curved mirror forms real images. The curved mirrors are classified in two types that are concave and convex. The convex reflects at an angle at edges and also forms a smaller distorted image than actual size while the concave are converging mirror which are similar to spoon shape. These types of mirrors form image when light is bounced by their curve up to a specific area. Here we are discussing about the concave mirror, its equation and properties, mirror images at various points, mirror ray diagram, and its uses.
As mentioned earlier, the curved mirrors are partial spherical surfaces. The line of symmetry of the curved mirror is called as the principal axis of the mirror. The radius of the sphere is called the radius of curvature and half radius of curvature of the mirror is called the focal length of the mirror. The focal length is also defined as the distance from the mirror along the principal axis to the point called ‘focus’ of the mirror.
Look at the above diagram. The mirror on the left has a bulging towards left, that is, towards the object. The focus in this case is on the other side of the mirror. On the other hand the mirror on the right is concave to the right and hence the focus of the mirror is at the same side as that of the object. The mirror on the left reflects out the ray, outward or diverges the incident ray. Hence this mirror is called as ‘diverging mirror’ or ‘convex mirror’. The image formed by a diverging mirror is virtual because the reflected rays only ‘appear’ to intersect behind the mirror. The mirror on the right side reflects out the ray, inward or converges the incident ray. Hence this mirror is called as ‘converging mirror’ or ‘concave mirror’. The image formed by a converging mirror is real because the reflected rays actually intersect before the mirror. However, if an object is placed within the focal length of a concave mirror, the mirror can produce only a virtual image but it is magnified.
Uses of Convex Mirror
If an object is placed within the focal length of a concave mirror, the mirror can produce a magnified virtual image. This property helps to use concave mirrors as magnifying reflectors. For example, you can study a wound on your face more clearly by keeping your face close to a concave mirror and the image will look much bigger compared to a plane mirror.
The light rays from a source placed on the focus of a concave mirror are reflected in such a ways that the reflected rays is parallel. This concept is used in hand torches operated by electric batteries, in the head lights of automobiles etc. Concave mirrors are also used in telescopes.
Uses of Concave Mirror
The convex mirrors diverge the light rays. As a result, the images produced are virtual and smaller in size. In addition, the images appear closer unlike in case of plane mirrors where the images are at the same distance as that of the object. The property that the images of a convex mirror are smaller in size helps to view more objects. This concept used in ‘search mirrors’ placed in big stores or community halls. The property that image of a convex mirror appear closer helps to concentrate on objects which are following us. This is the concept of rear view mirrors that are used in all automobiles.
Plane Mirror
A plane mirror is the simplest form of mirrors and the most commonly used. We look ourselves in front of a mirror at least a few times a day. In addition to the cosmetic purposes, plane mirrors have also important applications in medical, industrial and scientific fields.
As the name suggests the shape of a plane mirror is a plane area. It is made from a clear plane glass sheet, usually thin and pasted with suitable reflecting abrasive (for example, mercury) on one side. Once this pasting is done, then the glass becomes opaque but due to the reflecting property of the abrasive, the plane glass sheet becomes a plane glass reflector or a plane glass mirror.
Plane Mirror Reflection
Consider the above figure. MM’ is a plane mirror. The hatched surface shows the abrasive and hence the other surface is used as a reflecting surface. Consider a ray AO strikes the plane mirror at an angle AON with the normal ON to the surface at O. This angle is called as the Angle of Incidence. The ray is reflected by the plane mirror as ray OA’ and it is called Reflected Ray. The angle made by the reflected ray with the normal is called as angle of reflection. As per the fundamental law of reflection, the angle of incidence and the angle of reflection are always congruent.
ASSESSMENT
- Light interacts with matter as
(a) wave
(b) particle
(c) both A and B
(d) rays - Our eyes detect light in
(a) RGB form, Red Blue Green form
(b) ROYGBIV, rainbow color form
(c) The simple form of a particular color
(d) none of these ways - Symbol to represent speed of light in vacuum or air is
(a) v
(b) c
(c) a
(d) l - Mid-point between lens surface and principle axis is termed as
(a) midway center
(b) focal center
(c) focal point
(d) optical center - Light can travel in
(a) air only
(b) vacuum only
(c) both air and vacuum
(d) none of mediums
ANSWERS
- b
- b
- b
- d
- c
REFRACTION OF LIGHT
PHYSICS SS 2 Week 11
Topic: REFRACTION OF LIGHT
INTRODUCTION
When a ray travels from one transparent medium to another of different density, its direction is abruptly changed at the surface separating the two media. This is known as the refraction of the light ray. Thus a light ray appears to bend as it crosses the boundary of two different media. Refraction is due to the difference in the speed of light in the different media.
Refraction is the bending of a light ray as it crosses the boundary between two media of different densities, thus causes a change in direction.
The phenomenon of refraction is responsible for the following common observations: (i) The bottom of a clear river or pond appears shallower than it really is. (ii) A rod or spoon appears bent or broken when it is partially immersed in water or any liquid. (iii) Letters in prints seem to be nearer when we place a thick block of glass over them.
Laws of Refraction
Two laws are associated with refraction. The first law of refraction states that, the incidence, and the refracted ray all lie in the same plane.
The second law states that, the ratio of sine of the angle of incidence to the sine of the angle of refraction is constant for all rays passing from one medium to another.
The two lays of refraction were postulated by a physicsist called Snell. Snell’s first law of refraction is given as, Sin l/Sin r = n, a constant, for a given pair of media.
The law of refraction, which is generally known as Snell’s law, governs the behaviour of light-rays as they propagate across a sharp interface between two transparent dielectric media.
Consider a light-ray incident on a plane interface between two transparent dielectric media, labelled 1 and 2, as shown in the Fig below. The law of refraction states that the incident ray, the refracted ray, and the normal to the interface, all lie in the same plane. Furthermore,
n1 sin θ1 = n2 sin θ2,
where θ1 is the angle subtended between the incident ray and the normal to the interface, and θ2 is the angle subtended between the refracted ray and the normal to the interface. The quantities n1 and n2 are termed the refractive indices of media 1 and 2, respectively. Thus, the law of refraction predicts that a light-ray always deviates more towards the normal in the optically denser medium: i.e., the medium with the higher refractive index. Note that n1 > n2 in the figure. The law of refraction also holds for non-planar interfaces, provided that the normal to the interface at any given point is understood to be the normal to the local tangent plane of the interface at that point.
By definition, the refractive index of a dielectric medium of dielectric constant is given by
n = √K.
Table below shows the refractive indices of some common materials (for yellow light of wavelength λ = 589nm).
Refractive Indices of some common materials at λ = 589nm.
| Material | n |
| Air (STP) | 1.00029 |
| Water | 1.33 |
| Ice | 1.31 |
| Glass: | |
| Light Flint | 1.58 |
| Heavy Flint | 1.68 |
| Heaviest Flint | 1.89 |
| Diamond | 2.42 |
The law of refraction follows directly from the fact that the speed v with which light propagates through a dielectric medium is inversely proportional to the refractive index of the medium, v = c/n, where c is the speed of light in a vacuum. Consider two parallel light-rays, a and b, incident at an angle θ1 with respect to the normal to the interface between two dielectric media, 1 and 2. Let the refractive indices of the two media be n1 and n2 respectively, with n2 > n1. It is clear from the figure below that ray b must move from point B to point Q, in medium 1, in the same time interval, ∆t, in which ray amoves between points A and P, in medium 2. Now, the speed of light in medium 1 is v1 = c/n1, whereas the speed of light in medium 2 is v2 = c/n2. It follows that the length BQ is given by v1 ∆t, whereas the length AP is given by v2 ∆t. By trigonometry,
sin θ1 BQ/AQ = v1∆t/AQ,
and
sin θ2 AP/AQ = v2∆t/AQ
Hence sin θ1/ sin θ2 = v1/v2 =n2/n1
which can be rearranged to give Snell’s law. Note that the lines AB and PQ represent wave-fronts in media 1 and 2, respectively, and, therefore, cross rays and at right-angles.
Derivation of Snell’s law
When light passes from one dielectric medium to another its velocity changes, but its frequency f remains unchanged. Since, v = fλ for all waves, where λ is the wavelength, it follows that the wavelength of light must also change as it crosses an interface between two different media. Suppose that light propagates from medium 1 to medium 2. Let n1 and n2 be the refractive indices of the two media, respectively. The ratio of the wave-lengths in the two media is given by
λ2/λ1 = v2/f / v1/f = v2/v1 = n2/n1
Thus, as light moves from air to glass its wavelength decreases.
Again, the constant n, is known as the refractive index of the second medium with respect to the first medium. It is a number which gives a measure of refraction or bending of light as it travels from one medium to another. If light is travelling from air to glass, the refractive index of glass is given by
ang = sine of angle of incidence in air/sine of angle of refraction in glass
If light travels from glass to air then the refractive index gna = sine of angle of incidence in glass/sine of angle of refraction in air
From the principle of the reversibility of light we have:
ang = 1 / gna
Since refraction is due to the change in the speed of light as it travels from one medium to another, the refractive index is also given by
ang = speed of light in air (vacuum)/speed of light in glass
Terms Associated with Refraction
(i) The incident ray: This is the direction of rays of the light from the source to the first medium.
(ii) The refracted ray: This is the direction to which the light travels from the point of incidence to the second medium which is always denser than the first medium.
(iii) The angle of incidence: Thus is the angle at which the incident ray mixes with the normal in the first medium.
(iv) The angle of refraction: This is the angle at which the refracted ray mixes with the normal in the second medium.
Total Internal Reflection
Total internal reflection is a phenomenon that happens when a propagating wave strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, the wave cannot pass through and is entirely reflected. The critical angle is the angle of incidence above which the total internal reflectance occurs. This is particularly common as an optical phenomenon, where light waves are involved, but it occurs with many types of waves, such as electromagnetic waves in general or sound waves.
When a wave crosses a boundary between materials with different kinds of refractive indices, the wave will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the direction of propagation or ray is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the wave will not cross the boundary and instead be totally reflected back internally. This can only occur when the wave in a medium with a higher refractive index (n1) hits its surface that’s in contact with a medium of lower refractive index (n2). For example, it will occur with light hitting air from glass, but not when hitting glass from air.
The larger the angle to the normal, the smaller is the fraction of light transmitted rather than reflected, until the angle at which total internal reflection occurs. (The color of the rays is to help distinguish the rays, and is not meant to indicate any color dependence).
The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell’s law). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle θc is given by Snell’s law,
n1 sin θi = n2 sin θt.
Rearranging Snell’s Law, we get incidence
sin θi = n2/n1sin θt
To find the critical angle, we find the value for θi when θt = 90° and thus sin θt = 1. The resulting value of θi is equal to the critical angle θc.
Now, we can solve for θi, and we get the equation for the critical angle:
θc = θi = arcsin (n2/n1),
If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. If for example, visible light were traveling through acrylic glass (with an index of refraction of approximately 1.50) into air (with an index of refraction of 1.00), the calculation would give the critical angle for light from acrylic into air, which is
θc = arcsin (1.00/1.50) = 41.8o
Light incident on the border with an angle less than 41.8° would be partially transmitted, while light incident on the border at larger angles with respect to normal would be totally internally reflected.
If the fraction n2/n1 is greater than 1, then arcsine is not defined—meaning that total internal reflection does not occur even at very shallow or grazing incident angles.
So the critical angle is only defined when n2/n1 is less than 1.
Refraction of light at the interface between two media, including total internal reflection.
A special name is given to the angle of incidence that produces an angle of refraction of 90˚. It is called the critical angle.
ASSESSMENT
- When a ray of light enters a glass, and moves out of it. ray before it entered and ray after it left glass are
(a) perpendicular
(b) at a certain angle
(c) parallel
(d) at critical angle - If light enters glass, it slows down further to
(a) 200,000 km/s
(b) 150,000 km/s
(c) 100,000 km/s
(d) 50,000 km/s - Name given to change in speed of light is known as
(a) Reflection
(b) Critical change
(c) Refraction
(d) Rarefaction - Ray of light is always refracted in
(a) an indefinite direction
(b) a definite direction
(c) acute angle
(d) obtuse angle - Refraction of light is proved by
(a) Law of Einstein
(b) Law of light
(c) Law of Refraction
(d) Law of Thomas
ANSWERS
- c
- b
- c
- b
- c