The molar specific heat capacity of a gas is defined as the quantity of heat required to raise the temperature of 1 mole of the gas through 1K. Its unit is J mol-1 K-1.
Specific heat capacity of a gas may have any value between – ∞ and + ∞ depending upon the way in which heat energy is given.
Let m be the mass of a gas and C its specific heat capacity. Then ∆Q = m x C x ∆T where ∆Q is the amount of heat absorbed and ∆T is the corresponding rise in temperature.
So, C = ∆Q/m∆T
Case (i)
If the gas is insulated from its surroundings and is suddenly compressed, it will be heated up and there is the rise in temperature, even though no heat is supplied from outside
∆Q = 0
So, C = 0
Case (ii)
If the gas is allowed to expand slowly, in order to keep the temperature constant, an amount of heat ∆Q is supplied from outside,
then C = ∆Q/m∆T = ∆Q/O = + ∞
(∆Q is +ve as heat is supplied from outside)
Case (iii)
If the gas is compressed gradually and the heat generated ∆Q has conducted away so that temperature remains constant, then
C = ∆Q/m∆T = – ∆Q/O = – ∞
(∆Q is -ve as heat is supplied by the system)
Thus we find that if the external conditions are not controlled. the value of the specific heat capacity of a gas may vary from + ∞ to – ∞.
Hence, in order to find the value of specific heat capacity of a gas, either the pressure or the volume of the gas should be kept constant. Consequently, a gas has two specific heat capacities (i) Specific heat capacity at constant volume (ii) Specific heat capacity at constant pressure.
