Internal energy does or does not depend on volume of molecules?

[p3t3r1]

I am kind of confused by the conflict of the following two concepts.

If I understood correctly, internal energy of a system is independent of the volume occupied by the gas molecules. This is because the gas molecules are assumed to be ideal and therefore have no intermolecular interactions. (Hence volume doesn't matter)

This is proven to be true in adibatic change, where both volume and temperature changes.

If I understood correctly, this adibatic change can be divided into volume change at constant temperature, and temperature change at constant volume.

However, for the change in the internal energy, only the second step matters and hence delta U = Cv (Tf-Ti)

I fail to see how this applies in expansion work. In expansion work, delta U = w + q.

w = Pex x delta V for irreversible expansion

and

w = -nRTln(Vf/Vi) for isothermal reversible expansion.


Well if work is done, then the internal energy must change. So wouldn't this mean that the internal energy is dependent on the volume of the molecules?

(Unless of course the heat supplied by the surroundings is equal to the work done by the system to keep the process isotherma; and these two cancel each other out to give delta U = 0?)

Thanks!

 

[atyy]

(Unless of course the heat supplied by the surroundings is equal to the work done by the system to keep the process isotherma; and these two cancel each other out to give delta U = 0?)

Yes:
http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/isoth.html