Specific Heat of a Gas
For solids and liquids, we define the specific heat capacity as the quantity of energy that will raise the temperature of unit mass of the body by 1K. For gases, however, it is necessary to specify the conditions under which the change of temperature takes place, since a change of temperature will also produce large changes in pressure and volume.
The specific heat of gas can have many values, but out of them following two values are very important.
1) Specific heat at constant volume\(\left( {{C}_{V}} \right)\):
The specific heat of a gas at constant volume is defined as the quantity of heat required to raise the temperature of unit mass of gas through \({{1}^{0}}C\) (or) 1K when its volume is kept constant, i.e. \({{c}_{V}}=\frac{{{\left( \Delta Q \right)}_{V}}}{m\,\Delta T}\)
If instead of unit mass, 1 mole of gas is considered, the specific heat is called molar specific heat at constant volume and is represented by\({{C}_{V}}\).
\({{C}_{V}}=M{{c}_{V}}=\frac{M{{\left( \Delta Q \right)}_{V}}}{m\,\Delta T}=\frac{1}{\mu }\frac{{{\left( \Delta Q \right)}_{V}}}{\Delta T}\,\,\,\,\,\left( As,\,\mu =\frac{m}{M} \right)\)2) Specific heat at constant pressure\(\left( {{C}_{P}} \right)\):
The specific heat of a gas at constant pressure is defined as the quantity of heat required to raise the temperature of unit mass of gas through 1K when its pressure is kept constant, i.e.
\({{c}_{P}}=\frac{{{\left( \Delta Q \right)}_{P}}}{m\,\Delta T}\)If instead of unit mass, 1 mole of gas is considered, the specific heat is called molar specific heat at constant pressure and is represented by\({{C}_{P}}\).
\({{C}_{P}}=M{{c}_{P}}=\frac{M{{\left( \Delta Q \right)}_{P}}}{m\,\Delta T}=\frac{1}{\mu }\frac{{{\left( \Delta Q \right)}_{P}}}{\Delta T}\,\,\,\,\,\left( As,\,\mu =\frac{m}{M} \right)\)