The heat capacity of an ideal gas.

[corr0105]

The question states: For an ideal gas ∂U/∂V=0. Show that this implies the heat capacity $$_{}C$$V of an ideal gas is independent of volume.

I can't wrap my mind around how I could answer this question besides just stating the obvious. The expression for heat capacity is:
$$_{}C$$V=∂U/∂T (with v held constant)
The subscript V means that volume must be held constant and that heat capacity is only dependent only upon a changing temperature.

The chapter of my thermodynmaics book that this homework problem comes from is about Maxwell Relations, if that helps at all. However, all that helped me do was derive the fact that ∂U/∂V=0 but not actually answer the question.

Any help would be WONDERFUL! thanks so much! :)

 

[Astronuc]

Can one use

C_V=∂U/∂T = (∂U/∂V)(∂V/∂T)?

 

[corr0105]

I guess I'm not sure how exactly that works, but that would just make the heat capacity 0, which wouldn't necessarily answer the question.
Plus, volume is not a function of temperature, so that rule would not apply here... I don't believe.