Entropy Change of an Ideal Gas

[mouzis]

Homework Statement

Using the expression for the entropy change of an ideal gas when the volume and temperature change and TV^$\gamma-1$ = constant, show explicitly that the change in entropy is zero for a quasi-static adiabatic expansion from state V₁T₁ to state V₂T₂.

Homework Equations

TV^$\gamma-1$ = constant

dS = dQ_r / T

The Attempt at a Solution

My idea was to use T₁V₁^$\gamma-1$ = T₂V₂^$\gamma-1$ and solve for T in terms of V and substitute into the second equation. I couldn't figure it out from there, so my question is is my idea of what to do fundamentally wrong, or is my calculation once i set up the problem wrong?

 

[Chestermiller]

$$dS=C_v\frac{dT}{T}+R\frac{dV}{V}$$