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Chapter, , 4 | Calorimetry, , , , SYLLABUS, , (i) Calorimetry : Meaning, Specific heat capacities, Principle of method of mixture, Numerical problems on specific, heat capacity using heat loss and gain and the method of mixtures., , Scope of syllabus : Heat and its units (calorie, joule), temperature and its units (°C, K); Thermal (heat) capacity, C’=QIAT. (S.I. unit of C’), Specific heat capacity c = O/m AT; (S.I. unit of c), Mutual relations between heat capacity, and specific heat capacity, Values of c for some common substances (ice, water and copper). Principle of method of, mixtures including mathematical statement. Natural phenomena involving specific heat; consequences of high, , sp. heat of water. Simple numerical problems., , , , , , (ii) Latent heat; loss and gain of heat involving change of state for fusion only., , Scope of syllabus : Change of phase (state); heating curve for water; latent heat; sp latent heat of fusion (S.I. unit)., Simple numerical problems. Common physical phenomena involving latent heat of fusion., , , , , , (A) HEAT CAPACITY, SPECIFIC HEAT CAPACITY AND ITS MEASUREMENT, , , , 11.1 CONCEPT OF HEAT, , We know that each substance is made up of, molecules. The molecules in.a substance are in a, state’ of random motion and each molecule exerts, a force of attraction on the other molecules. Thus, molecules possess kinetic energy due to their, random motion and potential energy due to the, molecular attractive forces. The sum of the, potential energy and kinetic energy is called, their internal energy. The total internal energy of, molecules of a substance is called its heat energy., , A hot body has more internal energy than an, identical cold body. When a hot body is kept in, contact with a cold body, the cold body warms, up, while the hot body cools down. i.e., the, internal energy of the cold body increases, while, that of the hot body decreases. Thus there is a, flow of internal energy from the hot body to the, cold body when they are kept in contact. The, energy which flows from the hot body to the cold, body is called the heat energy or simply the heat., Thus, , , , Heat is the internal energy of molecules, constituting the body. It flows from a hot body, to a cold body when they are kept in contact., , Like all other forms of energy, heat is also a, measurable quantity. The measurement of the, quantity of heat is called calorimetry., , Units of heat, Like other forms of energy, the S.I. unit of, heat is joule (symbol J)., , The other most commonly used unit of heat, is calorie (symbol cal). It is defined as follows :, , , , , , , , , , , , , | One calorie is a UC y of heat energy, , rature of 1 g of water, , , , , , , , , , ‘through, , , , In the above definition, it has been assumed, that the heat energy required to raise the, temperature of 1 g of water through 1°C at each, initial temperature is same. However this is not, true due to non-uniform thermal expansion of, water. Hence the precise definition of calorie, , 256

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(which is also called 15°C calorie) is given as, follow :, , , , One calorie is the heat energy required to raise, the temperature of | g of water from 14-5°C to, 15-5°C., , , , The unit calorie is related to the S.I. unit joule, as follows :, , 1 calorie (or 1 cal) = 4-186 J or 4-2 J nearly*, , , , , , , , , , se L1- 1), , Sometimes, calorie is a smaller unit of heat,, so we use a bigger unit called the kilo-calorie, (symbol kcal), where, , 1 kilo-calorie = 1000 calorie = 4200 J nearly., , , , One kilo-calorie is the heat energy required to, raise the temperature of 1kg of water from, 14:5°C to 15-5°C., , The unit kilo-calorie is generally used for, measuring the energy value of foods., , 11.2 CONCEPT OF TEMPERATURE, , On keeping a hot body in contact with a cold, body, heat flows from the hot body to the cold, body due to which the hot body gets cooled,, while the cold body gets warmed., , The body which imparts heat is said to be at, a higher temperature than the body which receives, heat. Thus, temperature determines the direction, of flow of heat., , When a body receives heat energy, the, particles constituting the body start vibrating, more vigorously and so its temperature rises, provided its physical state or dimensions remain, unchanged., , Thus temperature is defined as below., , , , , , , , , , Temperature is a parameter which tells the, thermal state of a body (i.e., the degree of, hotness or coldness of body). It determines the, direction of flow of heat when two bodies at, different temperatures are placed in contact., , , , , , , , * For calculations, we generally take 1 cal = 4-2 J, , If there is no transfer of heat between the two, bodies placed in contact, they are said to be at, same temperature, but it does not mean that they, have equal amount of heat in them. In fact,, temperature alone does not tell us the quantity of, heat energy contained in a body. Experimentally,, we find that by imparting the same quantity of, heat energy to different bodies, they get heated to, different temperatures. The amount of heat energy, contained in a body depends on mass,, temperature and the material of body., , Unit of temperature, , The S.I. unit of temperature is kelvin, (symbol K). The other most common unit of, temperature is degree celsius (symbol °C). They, are related as :, , TK=273+t°C, , , , , , , , (11.2), , , , or more precisely, T K = 273-15 + t °C, , Thus by adding 273 (or 273-15) to the, temperature in degree celsius, we get the, temperature in kelvin. The zero of the kelvin scale, (called absolute zero or 0 K) is the temperature, at which the molecular motion ceases. It is equal, to -273°C (or -273-15°C)., , Thus a degree (or temperature difference) is, same on both the celsius and kelvin scales i.e.,, , At°C=ATK -(11,3), , , , , , , , , , 11.3 FACTORS AFFECTING THE QUANTITY, OF HEAT ABSORBED TO INCREASE, THE TEMPERATURE OF A BODY, , The quantity of heat energy absorbed to, increase the temperature of a body depends on, three factors : (1) mass of the body, (2) the, increase in temperature of the body, and, (3) the material (or substance) of the body., , Experimentally it is observed that, (1) Objects with different mass made from the, same substance absorb different amounts of, , heat energy to raise their temperature by the, same amount. For example, to raise the, , 257

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temperature of 1 kg of water by 1°C, heat, energy absorbed is 1 kcal, while to raise the, temperature of 2 kg of water by 1°C is, 2 kcal. Thus the amount of heat energy, absorbed is directly proportional to the mass, of the object ie, Qe m. a), , (2) Objects with equal mass made from the same, substance absorb different amounts of heat, energy to raise their temperature by different, amounts. For example, to raise the, temperature of 1 kg of water by 1°C, heat, energy absorbed is 1 kcal, while to raise the, temperature of same mass of water by 2°C is, 2 kcal. Thus the amount of heat energy, absorbed is directly proportional to the rise in, temperature Af ie, Qo At « (di), , (3) Objects of same mass but made from different, substances absorb different amounts of heat, , energy to raise their temperature by the same, amount. For example, if equal mass of water, and copper are heated through 1°C, the, amount of heat absorbed by water is nearly ten, times the amount of heat absorbed by copper., Thus, the amount of heat energy absorbed, depends on the substance of the object, which is expressed in terms of its specific heat, capacity c., , From the above observations (i) and (ii),, , Q «< mand Q « At, , or Q=cmAt (11.4), , , , , , , , , , where c is the constant of proportionality which, is called the specific heat capacity of the, substance. It is the characteristic of the, substance and is different for different, substances., , 11.4 DIFFERENCE BETWEEN HEAT AND TEMPERATURE, , , , Heat, , ‘Temperature, , , , 1. Heat is a form of internal energy obtained due to, random motion and attractive force of molecules in a, substance., , . The §.L. unit of heat is joule (J)., , . The amount of heat contained in a body depends on, mass, temperature and substance of body., , 4. Heat is measured by the principle of calorimetry., . Two bodies having same quantity of heat may differ in, their temperature., , 6. When two bodies are placed in contact, the total amount, of heat is equal to the sum of heat of individual body., , wn, , w, , , , , , . Temperature is a quantity which determines the, 2. The S.I. unit of temperature is kelvin (K)., . The temperature of a body depends on the average, , 4. Temperature is measured by a thermometer., . Two bodies at same temperature may differ in the, , . When two bodies at different temperatures are, , direction of flow of heat on keeping the two bodies, at different temperatures in contact., , kinetic energy of its molecules due to their random motion, |, , quantities of heat contained in them., , placed in contact, the resultant temperature is a, temperature in between the two temperatures,, , , , 11.5 THERMAL (OR HEAT) CAPACITY, , It is denoted by the symbol C’. Thus,, , , , (C’ = Q/AT), From our everyday experience we find that, , , , Heat capacity C’ =, , amount of heat energy supplied, risein temperature, , , , , , different bodies require different amounts of heat, energy for equal rise in their temperature. This, property of a body is expressed in terms of its, , wa(l.5), , If on imparting an amount of heat Q to a, , thermal (or heat) capacity. The heat capacity of body, its temperature rises through At °C (or At K),, a body is defined as follows : then ;, , , , The heat capacity of a body is the amount of, heat energy required to raise its temperature, , , , Heat capacity of the body C’ = 2 11.6), , , , , , , , , , by 1°C (or 1 K)., , , , 258

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Units of heat capacity, , The S.I. unit of heat capacity is joule per, kelvin (or J K~!). It is also written as joule per, degree C (or J °C-!)*., , The other common units of heat capacity, are cal °C“! (or cal K~!) and kcal °C“ (or keal K~!)., They are related as, f 1 keal °C! = 1000 cal °C!, , 1 cal K-71 =4.2 JK"!, , , , and, , , , , , , , Note : If the heat capacity of a vessel is, 30 J K-, it means that 30 J heat energy is, required to raise the temperature of that vessel, by 1 K (or 1°C)., , , , , , , , 11.6 SPECIFIC HEAT CAPACITY, , Heat capacity of a body when expressed for unit, mass is called its specific heat capacity. It is denoted, by the symbol c. Thus specific heat capacity of a, substance is defined as the heat capacity per unit, mass of a body of that substance, i.e.,, 1, , , , Heat capacity of body C”, , From egn. (11.9), heat energy required to raise, the temperature of a body of mass m kg by At K, is given as :, , , , Q=mx cx Atjoule ..(11.10), , , , , , , , Units of specific heat capacity, The S.I. unit of specific heat capacity is joule, , per kilogram per kelvin ( or J kg“! K~!) or joule, , per kilogram per degree celsius (or J kg"! °C-!),, The other units of specific heat capacity, , are cal g-! °C"! and kcal kg“! °C-!. These units, , are related as :, , 1 cal'g-! °C! = 1 kcal ke=! K, =42 x10? Jkg! Ko, , , , , , , , Note : If specific heat capacity of copper is, 0-4 J g-! K-, it means that the heat energy, required to raise the temperature of 1 g of copper, by 1 K (or 1°C) is 0-4 J., , Relationship between the heat capacity and, specific heat capacity, , From eqn. (11.7)., , , , , , Specific heat capacity c = Massornebeaym, , eeuhed)), , , , , , , , c=2, , From eqn. (11.2), M1, , , , 2} ais), , mx At, , , , «. Specific heat capacity c =, , , , , , , , In other words, we can define specific heat, capacity as follows :, , Heat capacity C’ = mass m x specific heat capacity c, , (11.11), , The above eqn. (11.11) relates the heat, , capacity C’ of a body to the specific heat, capacity c of its substance., , 11.7 DISTINCTION BETWEEN THE HEAT, , CAPACITY AND SPECIFIC HEAT CAPACITY, , , , , , , , , , Heat capacity, , Specific heat capacity, , , , The specific heat capacity of a substance is, the amount of heat energy required to raise the, temperature of unit mass of that substance, through 1°C (or 1 K). ie.,, Specific heat capacity, , amount of heat energy supplied, , , , , , , , c= “Mass x rise in temperature, (11.9), * Since S.I. unit of temperature is kelvin (K), so it is more, , appropiate to write the S.I. unit of heat capacity as, JK" instead of J °C., , , , 3,, , 4., , . It is the amount of heat, , energy required to raise, the temperature of entire, body by 1°C., , . It depends both on the, , substance and mass of the, body. More the mass of, the body, more is its heat, , capacity., Heat capacity C’ = £, , = mass m x specific heat, capacity c, , Its unit is J K-!., , 4, Its unit is J kg! K-),, , , , 1. It is the amount of heat, energy required to raise, the temperature of unit, mass of the body by 1°C., , 2. It does not depend on the, mass of the body, but it is, the characteristic property, of the substance of the, body., , 3. Specific heat capacity c, Q _ heatcapacity C’, mAt, , mass m, , , , , , 259

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11.8 SPECIFIC HEAT CAPACITY OF SOME, COMMON SUBSTANCES, , The specific heat capacity of a substance is, its characteristic property. It is different for, different substances. Usually a good conductor has, a low specific heat capacity, while a bad, conductor has a high specific heat capacity. If we, heat equal mass of two different substances on, the same burner so that the rate of heat supply, is same, we notice that after the same time, interval, the rise in temperature for the two, substances is different. This is because of their, different specific heat capacities. The substance, with low specific heat capacity shows a rapid and, high rise in temperature thus it is a better, conductor of heat than the substance with high, specific heat capacity which shows a slow and, small rise in temperature., , Water has an unusually high specific heat, capacity (= 4200 J kg! K"}).*, , Note : The specific heat capacity of the, same substance is different in its different, phases. The specific heat capacity of water is, 4200 J kg! K+, of ice is 2100 J kg! K"! and, of steam is 460 J kg! K7., , , , , , , , , , The specific heat capacity is maximum, equal, to 14630 J kg! K~! for hydrogen., , Specific heat capacity of some common substances, , , , * More precisely the specific heat capacity of water is, 4180 J kg“! K-!. But for convenience, its value is taken as, 4200 J kg! K-71., , a 260 PS ee, ~~., , 11.9 CALORIMETER, , A calorimeter is a cylindrical vessel which is, used to measure the amount of heat gained (or, lost) by a body when it is mixed with the other, body. It is shown in Fig. 11.1. It is made up of, a thin sheet of copper because (i) copper is a, good conductor of heat, so the vessel soon, acquires the temperature of its contents, and, (ii) copper has the low specific heat capacity so, the heat capacity of calorimeter is low and the, amount of heat energy taken by the calorimeter, from its contents to acquire the temperature of its, contents, is very small. The outer and inner, surfaces of vessel are polished so as to reduce the, loss of heat due to radiation. For insulation, it, is placed inside a wooden jacket. The space, between the calorimeter and the jacket is filled, with some poor conductor such as wool, cotton,, etc. to avoid the heat loss by conduction. It is, covered with a wooden lid to avoid the heat loss, by convection. The lid has two holes, one for the, stirrer (used to mix its contents properly) and the, other for the thermometer (to measure the, temperature of its contents)., , THERMOMETER, , , , , , , COPPER VESSEL, WOODEN, , JACKET, WOOL, , Fig. 11.1 Calorimeter, , 11.9 PRINCIPLE OF METHOD OF MIXTURES, (OR PRINCIPLE OF CALORIMETRY), , When a hot body is mixed (or is kept in, contact) with a cold body, heat energy‘passes, from the hot body to the cold body, till the, bodies attain the same temperature. If no heat, energy is lost to the surroundings (i.e., if the, system is perfectly insulated), then