# Carnot cycle, fundamental equation of ideal gas

1. Apr 24, 2012

### fluidistic

1. The problem statement, all variables and given/known data
Assuming that the auxiliary system in the Carnot cycle is a monoatomic ideal gas whose fundamental equation is $S=\frac{NS_0}{N_0} +NR \ln \left [ \left ( \frac{U}{U_0} \right ) ^{3/2} \left ( \frac{V}{V_0} \right ) \left ( \frac{N}{N_0} \right ) ^{-5/2} \right ]$.
1)Find the adiabats in a diagram T-V.
2)Sketch a P-V diagram of the cycle.
3)Describe the operation of a cycle as a refrigerator.
4)Describe the functionning of a Carnot cycle as a heat pump.

2. Relevant equations
$dS=0$.

3. The attempt at a solution
For 1) my strategy is to first use $dS=0= \frac{\partial S} {\partial N}dN+\frac{\partial S} {\partial U}dU+\frac{\partial S} {\partial V}dV$ then isolate V in function of T. But after having done all the derivatives, the remaining equation is still quite complicated.
Oh wait... there's no variable "T" inside it. Maybe I should get T as $\frac{1}{\frac{\partial S }{\partial U}}$? Then I consider all variables but "V" as constants? And then graph that function?

Edit: This cannot be, I get $T=\frac{2U}{3NR}$ that way. Absolutely no dependence between T and V...