Does Heating a Gas Under Constant Pressure or Volume Affect Its Internal Energy?

[Alvine]

Homework Statement
I have two identical volumes of gas, and I heat them both to 100 C, one under constant pressure, one under constant volume. Which has more internal energy after the process?



The attempt at a solution
I believe that they both have the same as the extra heat you have to put into the system at constant pressure to do the expansion is lost as work. But is it more complicated than this as T is changing?

Thanks

 

[phyzguy]

I think you're right. The internal energy of an ideal gas is just 3NkT/2, so since the two samples have the same N and the same T after heating them, they have the same internal energy. As you say, you have to put more heat into the constant pressure sample to source the PdV work, but the final internal energies should be the same.