The heat capacity specifies the heat needed to raise a certain amount of a substance by 1 K. For a gas, the molar heat capacity C is the heat required to increase the temperature of 1 mole of gas by 1 K.
Defining statement: dQ = nC dT
Important: The heat capacity depends on whether the heat is added at constant volume or constant pressure.
Why care about the difference?
Defining statement: dQ = nCV dT
1st Law of Thermodynamics gives: dQ = dE - dW = dE at constant volume.
|Thus dQ = dE = nCV dT =||
|nR dT ,|
|Comparing, we get, for a monatomic ideal gas: CV||=||
Since dQ = dE when the volume is
dE = n CV dT.