Page 1 :
THERMAL PROPERTIES OF MATTER, , Chapter 11, , THERMAL PROPERTIES OF MATTER, , Temperature: Temperature is relative measure or indication of hotness or coldness of a body., Temperature of a body determines the direction of flow of energy. The S I unit of temperature is, kelvin (K). 0C is a commonly used unit of temperature., Heat: Heat is the form of energy transferred between two systems or a system and its, surroundings by virtue of temperature difference., Heat energy flows from body of higher temperature to a body of lower temperature. Heat, gained by a body is taken as positive while heat lost by a body is taken as negative. S I Unit of heat, energy is joule (J)., Thermometry: The branch of science which deals with the measurement of temperature of a, substance is known as thermometry., Thermometer: A device used to measure the temperature of a body is called thermometer., Commonly used thermometers are liquid-in-glass type. Mercury and Alcohol are the liquids in, most of this type of thermometer., Principle of Thermometer: The principle of thermometer is, when a substance is heated, some of, its physical properties change., The commonly used property is variation of the volume of a liquid with temperature., Temperature scales: To measure temperature of a body different temperature scales are defined., Each has two fixed points. The ice (freezing) point and steam (boiling) point of water are the two, convenient fixed points., (i) Celsius scale (0C): Celsius scale of temperature was invented by Andres Celsius. In this scale,, the melting point of pure ice at standard atmospheric pressure is 00C and marked as lower fixed, point. The boiling point of pure water at standard atmospheric pressure is 1000C and marked as, upper fixed point. The interval between these two points is divided into 100 equal parts. Each part, is taken as “One degree Celsius”., (ii) Fahrenheit scale (0F): Fahrenheit scale was invented by Gabriel Fahrenheit. In this scale, the, melting point of pure ice at standard atmospheric pressure is 320F and marked as lower fixed, point. The boiling point of pure water at standard atmospheric pressure is 2120F and marked as the, upper fixed point. The interval between these two points is divided into 180 equal parts and each, part is known as “One degree Fahrenheit”., Relation between Celsius and Fahrenheit scale:, A plot of Fahrenheit temperature ( ) versus Celsius, temperature ( ) is as shown., The equation of the straight line is given by,, , Karnataka PUC Physics Telegram channel, , Page | 1

Page 2 :
THERMAL PROPERTIES OF MATTER, , Drawbacks of liquid-in-glass thermometers: Liquid in glass thermometers shows different, readings for the temperatures other than the fixed points. This is because of different expansion, properties of liquids., This problem can be removed, if a thermometer uses a gas. They give same reading, regardless of which gas is used and experiments show that that all gases at low densities exhibit, same expansion behaviour., Gas laws: The laws which describe the behaviour of a gas at different conditions are called gas, laws and the behaviour of a given quantity of gas is explained using the variables such as pressure,, volume and temperature., Boyle’s law: When temperature is held constant, the volume of a given mass of gas is inversely, proportional to its pressure., , Charles law: At constant pressure, the volume of a given mass of an ideal gas is directly, proportional to its absolute temperature., , Ideal Gas equation: For low density gases, we can combine Boyle’s law and Charles law into a, single relationship as,, , This equation is called Ideal gas equation. Where R is a constant called universal gas constant and, , Absolute Temperature: From the Ideal gas, equation, we have, . This relationship allows, a gas to be used to measure temperature in constant, volume gas thermometer., At constant volume, P versus T graph is as, shown. The relationship is linear over a large, temperature range. It looks as pressure might reach zero, with decreasing temperature and gas, remains to be a gas. Thus, pressure of a gas becomes zero at, ., Karnataka PUC Physics Telegram channel, , Page | 2

Page 3 :
THERMAL PROPERTIES OF MATTER, , Absolute zero: The temperature at which the pressure of an ideal gas becomes zero is termed as, absolute zero., Kelvin’s scale of temperature: This scale was suggested by Kelvin. Absolute zero is foundation of, the Kelvin temperature scale. The zero of the absolute scale of temperature is denoted by, and, known as absolute zero., Hence,, Ice point in Kelvin scale is 273.15 K, Boiling point in Kelvin scale is 100+273.15=373.15 K, Practically,, Effects of Heat: The common effects of Heat are,,  Thermal expansion,  Rise in temperature,  Change in state, Thermal expansion: The increase in dimensions of a body due to increase in its temperature is, called thermal expansion., There are three types of thermal expansion.,  Linear expansion,  Area expansion,  Volume expansion, Linear expansion: The expansion in length is called linear expansion., When a rod like solid is heated its length increases., The increase in length ( ) is directly proportional to, (i) its original length ( ), (ii) the change in temperature (, Mathematically,, , Where, , ), , constant and called co-efficient of linear expansion., , Co-efficient of linear expansion: It is defined as the increase in length per unit length per degree, increase in temperature., S I unit of Co-efficient of linear expansion is, . It is also expressed in 0, ., Note: (i) The increase in length ( ) is also depends on the material of the solid., (ii) Normally metals expand more and have relatively high values of, Thermal stress: Consider a metallic rod whose ends are fixed rigidly. When the temperature of the, rod increases, its length increases. Since there is no space left to increase its length, so it bends. If, the rod is not allowed to bend, then it will be under a great stress. This is known as thermal stress., , Karnataka PUC Physics Telegram channel, , Page | 3

Page 4 :
THERMAL PROPERTIES OF MATTER, , Expression for thermal stress:, Let be the length of the rod and be its cross-sectional area., be the co-efficient of linear expansion of the material of the rod., Let, be the increase in temperature and be the increase in its length., , This is the expression for thermal stress developed in the rod., Force developed in the rod due to Thermal stress:, , Force,, , This is the expression for force developed in the rod., Area (Superficial) expansion: The expansion in the area is called area expansion., When a planar body like solid is heated its area increases., The increases in area ( ) is directly proportional to, (i) its original area ( ), (ii) its change in temperature (, Mathematically,, , Where, , ), , constant and called co-efficient of area expansion., , Co-efficient of area expansion: It is defined as the increase in area per unit area per degree, increase in temperature., S I unit of Co-efficient of area expansion is, . It is also expressed in 0, ., Volume (Cubical) expansion: The expansion in the volume is called volume expansion., When a substance is heated its volume increases., The increases in volume ( ) is directly proportional to, (i) its original volume ( ), (ii) its change in temperature ( ), Mathematically,, , Where, , constant and called co-efficient of volume expansion., , Karnataka PUC Physics Telegram channel, , Page | 4

Page 5 :
THERMAL PROPERTIES OF MATTER, , Co-efficient of volume expansion: It is defined as the increase in volume per unit volume per, degree increase in temperature., S I unit of Co-efficient of volume expansion is, It is also expressed in, , 0, , ., , ., , Note: Co-efficient of volume expansion is not strictly a, constant. It depends on temperature. It is initially small and, rises sharply and becomes a constant at high temperature., Variation of Co-efficient of volume expansion ( ) with temperature – For SOLIDS and, LIQUIDS: At ordinary temperature Solids and Liquids expand less compared to the gases. For, liquids, the co-efficient of volume expansion is relatively independent of the temperature., Variation of Co-efficient of volume expansion ( ) with temperature – For GASES, For gases, is depend on temperature, which can be obtained as follows,, The ideal gas equation is given by,, At constant pressure, the equation becomes,, , It shows that, , decreases with increase in temperature., , Anomalous expansion of water: Water contracts on heating from 00C to 40C. This is known as, anomalous expansion of water., , In the temperature range of 00C to 40C, volume of water decreases as temperature increases., Hence, Co-efficient of cubical expansion of water is negative. Hence water has greatest density at, 40C. The graph below shows the variation of volume and density of water with temperature., Relation between, , and, , :, , (), , Karnataka PUC Physics Telegram channel, , Page | 5

Page 6 :
THERMAL PROPERTIES OF MATTER, , (, , ), , Squaring on both sides,, , (, , ), , (, , ), , Since, , is very small,, can be neglected., (, ), (, ), Comparing with the equation,, We have,, (ii) We have,, , (, , ), , Cubing on both sides,, , (, , ), , (, is very small,, and, (, ), Comparing with the equation,, We have,, , ), , Since, , can be neglected., (, , ), , Further,, Heat Capacity (S): Heat capacity of a substance is defined as the amount of heat required to raise, the temperature of the substance through, ., The S I unit is, (, ), The Quantity of heat required to warm a given substance depends upon its change in temperature, That is,, , Note: The Quantity of heat required to warm a given substance also depends upon (i) its mass ( ), and (ii) nature of the material of the substance, Specific heat capacity (s): Specific heat capacity of a substance is defined as the amount of heat, required to raise the temperature of unit mass of substance through, Specific heat capacity is also defined as heat capacity per unit mass., The S I unit is, , Note: Specific heat capacity of a substance depends on,, , ., , (i) nature of the material, (ii) raise or fall in temperature (, , ), , Molar specific heat capacity: It is defined as the amount of heat required to raise the temperature, of one mole of substance through, ., , The S I unit is, Karnataka PUC Physics Telegram channel, , Page | 6

Page 7 :
THERMAL PROPERTIES OF MATTER, , Specific heat of a gas: Solids and liquids have very small co-efficient of expansion. Therefore,, amount of heat spent in their expansion is negligible and heat supplied is assumed to increase only, the temperature., Gases have very large co-efficient of expansion. Therefore, amount of heat supplied to a gas, is used in two parts, (i) to raise the temperature of gas and, (ii) to do mechanical work by the gas, When heat is supplied to a gas, the increase in temperature of the gas is accompanied either by, increase in pressure or volume or both., Thus a gas can be heated under two conditions:, (i) at constant volume and, (ii) at constant pressure, Therefore, we consider the specific heat of a gas at constant volume ( ) or the specific heat of a, gas at constant pressure ( )., Specific heat capacity at constant volume (, , ): It is defined as, the amount of heat required to, , raise the temperature of unit mass of gas through, , at constant volume., , Specific heat capacity at constant pressure ( ): It is defined as, the amount of heat required to, raise the temperature of unit mass of gas through, at constant pressure., Note: (i), (ii), , is greater than, This relation is called Mayer’s relation., , Change of state: Matter normally exists in three states: solid, liquid and gas. A transition from one, state to another is called change of state., Melting: The change of state from solid to liquid is called melting., During this change of state temperature remains constant. That is both the solid and liquid states, of the substance co-exist in thermal equilibrium during this change of state., Melting point: The temperature at which the solid and liquid co-exist in thermal equilibrium, during change of state from solid to liquid is called melting point., Fusion: The change of state from liquid to solid is called fusion or freezing., Effect of pressure on melting point; Regelation: When a metallic wire carrying two masses on, either ends is hung from an ice cube, the wire passes through the ice cube without splitting it. This, phenomenon is called regelation., This is because ice melts at lower temperature due to increase in pressure. That is melting, point decreases with increase in pressure on ice., Note: Skating on ice is possible due to increase of pressure on it., Vaporisation: The change of state from liquid to vapour (gas) is called vaporisation., During vaporisation temperature remains constant and liquid and vapour state co-exist in thermal, equilibrium., Karnataka PUC Physics Telegram channel, , Page | 7

Page 8 :
THERMAL PROPERTIES OF MATTER, , Boiling point: The temperature at which the liquid and the vapour states of the substance co-exist, is called boiling point., Effect of pressure on boiling point: Boiling point of the substance increases with increase in, pressure. This effect is used in the construction of pressure cooker., Note: At high altitudes, atmospheric pressure is lower and reduces the boiling point of water. This, is why cooking is difficult on hills., Sublimation: The change from solid state to vapour state without passing through the liquid state, is called sublimation. Ex: Dry ice (solid, ), camphor etc., Triple point: The temperature at which the solid, liquid and vapour co-exist in thermal, equilibrium is called triple point., Latent heat: The amount of heat transferred per unit mass during the change of state of the, substance is called latent heat., If is the mass of the substance that undergoes a change from one state to the other, then, the quantity of heat required is given by,, where, latent heat, S I unit of latent heat is, (, ), Types of latent heat:, (i) Latent heat of fusion (, , ): The amount of heat required to melt unit mass of solid completely at, , its melting point is called latent heat of fusion., (ii) Latent heat of vaporisation ( ): The amount of heat required to vaporise unit mass of liquid, completely at its boiling point is called latent heat of vaporisation., The graph between temperature and amount of heat supplied for water is as shown., , Calorimetry: The branch of science which deals with the measurement of heat is called, Calorimetry., Principle Calorimetry: Heat lost by the hot body is equal to the heat gained by the colder body,, when they are kept in contact with each other, provided no heat is allowed to escape to the, surroundings., Calorimeter: A device in which heat measurement can be made is called Calorimeter., Karnataka PUC Physics Telegram channel, , Page | 8

Page 9 :
THERMAL PROPERTIES OF MATTER, , Calorimeter is a hollow cylinder made of copper with a lid and a stirrer placed in it. The, calorimeter is placed in an insulated enclosure so that there is no loss of heat by radiation., Transfer of heat: Heat transfers from a body at higher temperature to a body at lower, temperature. There are three modes of heat transfer, (i) Conduction, (ii) Convection, (iii) Radiation, Conduction: It is the mechanism of transfer of heat between two adjacent parts of a body because, of their temperature difference. In this mode of heat transfer, transfer of heat takes place without, any actual movement of the particles of the medium., Law of Thermal conductivity: The amount of heat that flows from hotter part to colder part is,,  directly proportional to area of cross-section ( ) of the body.,  directly proportional to the temperature difference (, ) between the hotter part and, colder part.,  directly proportional to the time ( ) for which heat flows.,  inversely proportional to the distance ( ) between the parts., (, ), (, (, where, , ), ), , constant, called Thermal conductivity, , Thermal conductivity: It is defined as the rate of flow of heat per unit area of its surface normal to, the direction of heat flow under unit temperature gradient., S I unit of thermal conductivity is, . Dimensions are, Classification of substance based on thermal conductivity:, (a) Good conductors of heat: These substances have large values of thermal conductivity., Ex: Most metals., For Ideal conductor thermal conductivity,, (b) Bad conductors of heat: These substances have small values of thermal conductivity., Ex: wood, air, wool, etc., For ideal bad conductor thermal conductivity,, Applications of thermal conduction:,  In winter, the iron chairs appear to be colder than the wooden chairs.,  Cooking utensils are made of aluminium and brass whereas their handles are made of wood.,  We feel warm in woollen cloths.,  Houses made of concrete roofs get very hot during summer days.,  Steel utensils with copper bottom are good for uniform hearting of food., Convection: It is the process in which heat is transferred by the actual movement of the particles of, the medium., Karnataka PUC Physics Telegram channel, , Page | 9

Page 10 :
THERMAL PROPERTIES OF MATTER, , Convection is possible only in fluids. Convection can be natural or forced. Natural convection is, responsible for many familiar phenomena such as sea breeze, land breeze, trade wind., Winds: In day time, earth is heated by the sun and hence air in contact with the earth gets heated, up. This heated air, being lighter, rises up and is replaced by the cold and heavier air from large, reservoir of water creating a sea breeze. At night this cycle is reversed forming land breeze., Trade winds: The equatorial and polar regions of the earth receive unequal solar heat. Air at the, earth surface near the equator is hot while the air in the upper atmosphere of the poles is cool. The, cold air from the poles rushes towards the equator whose pressure is low. Thus, convection, current of air starts between the equator and the poles. Due to rotation of earth from west to east,, the convection current drifts towards the east. Convection current blows from North-east towards, the equator, which is called Trade wind., Radiation: Radiation is the process in which heat is transferred from one region to another without, the necessity of any intervening medium., Radiation also refers to the energy emitted by a body and energy is emitted in the form of, electromagnetic waves. Energy so radiated/emitted is called Radiant energy., Thermal radiation: Everybody emits energy in the form of waves due to its temperature. These, waves are known as thermal radiations., Properties of thermal radiations:,  They travel along straight line at the seed of light.,  They can travel in vacuum.,  They do not heat intervening medium.,  They can be reflected and refracted.,  They exhibit the phenomenon of interference, diffraction and polarisation.,  They obey inverse square law that is their intensity varies inversely as the square of the, distance from the source., Note: Thermal radiations can be detected by thermopile, radiometer and bolometer., Black body: A body that absorbs all the radiations falling on it is called a black body., Black body radiation: Radiations emitted by a black body are called black body radiations., A black body at a given temperature emits all possible wavelengths at that temperature. The, intensity and wavelength emitted are independent of the material of the black body but depend, only on the temperature of the body., At low temperature, the wavelengths of the radiation emitted are in the infrared region. As the, temperature of the black body is increased to about, , the emitted wavelength corresponds to, the red region. At sufficiently high temperatures (, ), the emitted radiations contain shorter, wavelengths., The black body radiation consists of a continuous distribution of wavelengths covering, infrared, visible and ultraviolet portions of the electromagnetic waves., , Karnataka PUC Physics Telegram channel, , Page | 10

Page 11 :
THERMAL PROPERTIES OF MATTER, , Wien’s displacement law: According to this law, the wavelength ( ), corresponding to, maximum intensity of emission of black body radiation is inversely proportional to absolute, temperature of the black body., , Where, , is constant, called Wien’s constant and, , Note:, (i) The colour of a piece of iron heated first becomes dull red, then reddish yellow and finally, white hot. This can be explained using Wien’s displacement law., (ii) Wien’s displacement law is used to find the temperature of Sun and stars., Stefan’s Law (Stefan-Boltzmann law): Energy emitted by a black body per unit time per unit area, is directly proportional to the fourth power of the temperature., Mathematically,, Where is called Stefan-Boltzmann constant and, This law is obtained experimentally by Stefan and later proved theoretically by Boltzmann., Therefore it is also called as Stefan-Boltzmann law., Note:, (i) For a body other than black body, the energy radiated per unit time is given by,, (ii) A body at temperature , with surroundings at temperature , emits as well as receives, (, ), energy, the net rate of loss of radiant energy is,, Where, , emissivity of black body, , Emissivity: Emissivity of a body is defined as the ratio of the heat energy radiated per second per, unit area by the body to the amount of heat energy radiated per second per unit area by a perfect, black body at the same temperature., Emissivity of black body is one., Greenhouse effect: The earth surface is a source of thermal radiation. Large portion of this, radiation is absorbed by greenhouse gases, namely carbon di oxide (, ), methane (, ), nitrous, oxide (, ), chlorofluorocarbon (, ) and atmospheric ozone ( ). This heats up the, atmosphere which in turn, gives more energy to earth resulting in warmer surface. This heating up, of earth’s surface and atmosphere is known as greenhouse effect., Consequences of Greenhouse effect: Greenhouse effect heats up the earth’s surface and, atmosphere. Human activities have increased the greenhouse gases, resulting in increase in the, average temperature of earth by, to, . Without greenhouse effect, the temperature of the, earth would have been, . It has been estimated that, if such activities continue, then the, temperature of the earth will increase by, to, after 50 to 60 years., This global warming may cause problem for human life, plants and animals. Because of, global warming, ice caps are melting faster, sea level is rising and weather pattern is changing., Many coastal cities are at the risk of getting submerged. The enhanced Greenhouse effect may also, result in expansion of deserts., Karnataka PUC Physics Telegram channel, , Page | 11

Page 12 :
THERMAL PROPERTIES OF MATTER, , Newton’s law of cooling: The rate of loss of heat by a body is directly proportional to the, temperature difference between the body and the surrounding., Explanation:, Consider a body of mass and specific heat capacity at temperature, Let be the temperature of the surroundings of the body., (, (, , ), , (, , ), , ., , ), , ( ), , Let the temperature of the body decreases by, Heat lost by the body is,, , in time, , ., , ( ), ( ), , ( ), , (, , ), , (, , ), ∫, , (, , (, , (, , ), , ), , ∫, , ), , where, This equation shows a straight line having a negative slope., The graph between, , (, , Karnataka PUC Physics Telegram channel, , ) and time is as shown., , Page | 12

Page 13 :
THERMAL PROPERTIES OF MATTER, , Suggested Questions., One Mark., 1. State Charles law., 2. What is Ideal gas?, 3. Mention the relation between Celsius scale and Fahrenheit scale of temperature., 4. Mention the relation between Celsius scale and Kelvin scale of temperature., 5. What is anomalous expansion of water?, 6. Define heat capacity., 7. Mention the principle of calorimetry., 8. What is regelation?, 9. What is a black body?, 10. State Wien’s displacement law., 11. State Stefan’s law., 12. What is greenhouse effect?, 13. Give an example for greenhouse gas., Two Marks., 1. Differentiate between heat and temperature., 2. Show that, for an ideal gas., 3. What are the effects of heat?, 4. Define specific heat capacity and mention its SI unit., 5. State and explain Newton’s law of cooling., Three Marks., 1. Define three types of thermal expansions., 2. Derive, , for an ideal gas, where the symbols have their usual meaning., , 3. Define coefficient of linear expansion, coefficient of area expansion and coefficient of volume, expansion., 4. Plot a graph of temperature versus heat showing the changes in the states of ice on heating at, one atmospheric pressure. Indicate how much energy is absorbed in the two changes of states., 5. Mention the modes of heat transfer., 6. Explain the thermal conduction and hence define co-efficient of thermal conductivity., 7. Write any three properties of heat radiation., 8. Explain greenhouse effect., Five Marks., 1. Write a note on Kelvin scale of temperature., 2. Define specific heat of a gas at constant pressure and at constant volume. Give the relation, between them. Define latent heat of fusion and vaporisation., 3. State and explain law of thermal conductivity. Define coefficient of thermal conductivity., Mention its unit and dimension., 4. State and explain Newton’s law of cooling., , Karnataka PUC Physics Telegram channel, , Page | 13

Page 14 :
THERMAL PROPERTIES OF MATTER, , Numerical Problems., 1. A brass boiler has a base of area, and thickness, . It boils water at the rate of, , when placed on a gas stove. Estimate the temperature of the part of the flame in, contact with the boiler. Given that thermal conductivity of brass, and latent, heat of vaporisation of water, ., 2. What is the temperature of steel-copper junction in steady state? Length of steel rod, ,, length of copper rod, , temperature of free end of steel rod is, , temperature of free, and of copper rod is, . Area of cross-section of steel rod is twice that of copper rod. K of, steel, . K of copper, ., 3. A cubical ice box of thermocol has each side, and thickness of, ,, of ice is put in, the box. If outside temperature is, and co-efficient of thermal conductivity is, . Calculate the mass of ice left after, . Take latent heat of fusion of ice is, ., 4. A, drilling mechine is used to drill a boar in a small aluminium block of mass, ., How much is the raise in temperature of the block in, assuming, of power is, used up in heating. The machine itself or lost to the surroundings. Specific heat of aluminium, is, ., 5. Two pieces of copper and aluminium of equal thickness and cross sectional area are soldered, together. The other end of copper is kept at, and aluminium at, . Find athe, temperature of the interface if the thermal conductivities of copper and aluminium are, and, respectively., 6. Two identical iron and brass bars are soldered end to end. The free ends of iron bar and brass, bar are maintained at ends of iron bar and brass bar are maintained at, respectively., Calculate the temperature of the junction. (Given that, 7. How much heat is required to convert, of ice at, heat of ice, , . Latent heat of steam, , . Specific heat of water, , Karnataka PUC Physics Telegram channel, , )., into steam at, , . Given specific, , and latent heat of fusion of ice is, ., , Page | 14