JEE Main & Advanced Physics Kinetic Theory of Gases Specific Heat (\[{{C}_{P}}\] and \[{{C}_{V}}\]) of a Gas

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 \[({{C}_{V}})\] : 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 \[{{1}^{o}}C\] or  1 K when its volume is kept constant, i.e., \[{{c}_{V}}=\frac{{{(\Delta Q)}_{V}}}{m\Delta T}\]

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 capital \[{{C}_{V}}\].

\[{{C}_{V}}=M{{c}_{V}}=\frac{M{{(\Delta Q)}_{V}}}{m\Delta T}=\frac{1}{\mu }\frac{{{(\Delta Q)}_{V}}}{\Delta T}\]                \[\left[ \text{As }\mu =\frac{m}{M} \right]\]

(2) Specific heat at constant from \[({{C}_{P}})\] : 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 1 K when its pressure is kept constant, i.e., \[{{c}_{P}}=\frac{{{(\Delta Q)}_{p}}}{m\Delta T}\]

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 \[{{C}_{P}}\].

\[{{C}_{p}}=M{{C}_{p}}=\frac{M{{(\Delta Q)}_{p}}}{m\Delta T}=\frac{1}{\mu }\frac{{{(\Delta Q)}_{p}}}{\Delta T}\]               

\[\left[ \text{As }\mu =\frac{m}{M} \right]\]