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208 PHYSICS 10.6 SPECIFIC HEAT CAPACITY heat absorbed or given off to change the temperature of unit mass of it by one unit. This Take some water in a vessel and start heating it on a burner. Soon you will notice that bubbles quantity is referred to as the specific heat begin to move upward. As the temperature is capacity of the substance. raised the motion of water particles increases If ∆Q stands for the amount of heat absorbed or given off by a substance of mass m when it till it becomes turbulent as water starts boiling. undergoes a temperature change ∆T, then the What are the factors on which the quantity of heat required to raise the temperature of a specific heat capacity, of that substance is given substance depend? In order to answer this by question in the first step, heat a given quantity s =S = 1 ∆Q (10.11) of water to raise its temperature by, say 20 °C m m ∆T and note the time taken. Again take the same The specific heat capacity is the property of amount of water and raise its temperature by the substance which determines the change in 40 °C using the same source of heat. Note the the temperature of the substance (undergoing time taken by using a stopwatch. You will find it no phase change) when a given quantity of heat takes about twice the time and therefore, double is absorbed (or given off) by it. It is defined as the the quantity of heat required raising twice the amount of heat per unit mass absorbed or given temperature of same amount of water. off by the substance to change its temperature In the second step, now suppose you take by one unit. It depends on the nature of the double the amount of water and heat it, using substance and its temperature. The SI unit of the same heating arrangement, to raise the specific heat capacity is J kg K . temperature by 20°C,youwillfindthetimetaken If the amount of substance is specified in is again twice that required in the first step. terms of moles µ, instead of mass m in kg, we In the third step, in place of water, now heat can define heat capacity per mole of the the same quantity of some oil, say mustard oil, substance by and raise the temperature again by 20 °C. Now note the time by the same stopwatch. You will (10.12) find the time taken will be shorter and therefore, the quantity of heat required would be less than where C is known as molar specific heat capacity of the substance. Like S, C also that required by the same amount of water for depends on the nature of the substance and its the same rise in temperature. temperature. The SI unit of molar specific heat The above observations show that the quantity –1 –1 of heat required to warm a given substance capacity is J mol K . However, in connection with specific heat depends on its mass, m, the change in capacity of gases, additional conditions may be temperature, ∆T and the nature of substance. needed to define C. In this case, heat transfer The change in temperature of a substance, when a given quantity of heat is absorbed or rejected can be achieved by keeping either pressure or by it, is characterised by a quantity called the volume constant. If the gas is held under constant pressure during the heat transfer, then heat capacity of that substance. We define heat it is called the molar specific heat capacity at capacity, S of a substance as constant pressure and is denoted by C . Onp S = ∆Q (10.10) the other hand, if the volume of the gas is ∆T maintained during the heat transfer, then the where ∆Q is the amount of heat supplied to corresponding molar specific heat capacity is the substance to change its temperature from T calledmolar specific heat capacity at constant to T + ∆T. volume and is denoted by C . Fvr details see You have observed that if equal amount of Chapter 11. Table 10.3 lists measured specific heat is added to equal masses of different heat capacity of some substances at atmospheric substances, the resulting temperature changes pressure and ordinary temperature while Table will not be the same. It implies that every 10.4 lists molar specific heat capacities of some substance has a unique value for the amount of gases. From Table 10.3 you can note that water Reprint 2026-27