When I took this class years ago, I simply accepted it as fact. However, now that I'm teaching it, the following bugs me....a lot.
Why do they use Cv to describe the change of internal energy during the carnot cycle?
http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Thermodynamic_Cycles/Carnot_Cycle
There is obviously a volume change. But it is defined that $\Delta U = n*Cv*\Delta T$. How do you justify the use of Cv when there's a volume change?