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**1. Homework Statement**

Using the expression for the entropy change of an ideal gas when the volume and temperature change and TV

^{[itex]\gamma-1[/itex]}= constant, show explicitly that the change in entropy is zero for a quasi-static adiabatic expansion from state V

_{1}T

_{1}to state V

_{2}T

_{2}.

**2. Homework Equations**

TV

^{[itex]\gamma-1[/itex]}= constant

dS = dQ

_{r}/ T

**3. The Attempt at a Solution**

My idea was to use T

_{1}V

_{1}

^{[itex]\gamma-1[/itex]}= T

_{2}V

_{2}

^{[itex]\gamma-1[/itex]}and solve for T in terms of V and substitute in to 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?