Why is molar specific heat at constant pressure higher than at constant volume?

[chound]

Aren't we doing some work to prevent the gas from expanding if we maintain the constant volume. So shouldn't molar specific heat at constant pressure be equal to constant volume?

 

[Stephan Hoyer]

You don't do work with a change in pressure, but rather a change in volume:

dW = PdV

Since work is done in the constant pressure case but not the constant volume one, Cp and Cv are different.

 

[Meir Achuz]

The force preventing the expansion is stationary. Only a moving force can do work.