thermodynamics - Specific heat capacity at constant volume VS constant pressure

For an ideal gas, why is the specific heat capacity at constant volume lower than the specific heat capacity at constant pressure?

Answer

The simple answer, which is what I think you're hoping for is the following: At constant volume, the system (by definition) is not able to do work on the surroundings because work involves a change in volume. All the heat you put in is spent raising the temperature (internal energy).

At constant pressure, some of the energy you put in goes into raising the temperature (internal energy) and some of it goes into doing work by expanding the ideal gas.

Thus, the temperature increase is smaller in the constant pressure case than in the constant volume case. This is equivalent to saying that the specific heat capacity at constant pressure is larger than the specific heat capacity at constant volume.