Specific Heat of Gas :Molar Specific Heat of a Gas at Contant volume and Pressure
Specific Heat : Defination
If a substance has mass m, and the amount of heat required to change its temperature by $\Delta T$ is $\Delta Q$ , then the specific heat is given by:
$s = \frac{\Delta Q}{m \Delta T}$
Unit : $ J \cdot kg^{-1} \cdot K^{-1}$
That is, specific heat is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.
Molar Specific Heat :
When the quantity of a substance is expressed in moles (n) instead of grams, the heat required per mole is called the molar specific heat (C):
$C = \frac{\Delta Q}{n \Delta T}$
Here, C is called the molar heat capacity. It does not depend on the amount of the substance, but rather on: the conditions under which heat is supplied, the nature of the substance,and its temperature.
Unit: $J \cdot mol^{-1} \cdot K^{-1}$
Molar Specific Heat of a Gas}
The molar specific heat of a gas is defined under two conditions:
(i) At Constant Volume $( C_v)$ :
The amount of heat required to raise the temperature of 1 mole of a gas by 1°C at constant volume is:
$C_v = \left( \frac{\Delta Q}{\Delta T} \right)_v$
(ii) At Constant Pressure $( C_p)$
The amount of heat required to raise the temperature of 1 mole of a gas by 1°C at constant pressure is:
$C_p = \left( \frac{\Delta Q}{\Delta T} \right)_p$
Important Relation for Ideal Gases
$C_p - C_v = R$
Where \( R \) is the universal gas constant:
$R = 8.314 \, J \cdot mol^{-1} \cdot K^{-1}$