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**Thermodynamics - adiabatic process**

## Homework Statement

The question is: Consider a hypothetical ideal gas with internal energy U = NkT

_{o}(T/T

_{0})

^{α+1}, where T

_{o}and α are positive constants. Show that in an adiabatic process, V*exp[(1+1/α)(T/T

_{o})

^{α}] = constant.

## Homework Equations

PV

^{γ}= constant

γ = C

_{p}/C

_{v}

C

_{p}= C

_{v}+ Nk

## The Attempt at a Solution

I'm pretty sure that I'm supposed to show that [(1+1/α)(T/T

_{o})

^{α}] is equal to γ and since PV

^{γ}= constant, V*exp[(1+1/α)(T/T

_{o})

^{α}] = constant. When I try to solve it though I can't get the solution to come out. I differentiate U to get C

_{v}= Nk(1+α)(T/T

_{o})

^{1+α}. When I plug that into γ I get γ = 1 + 1/[(1+α)(T/To)

^{α}]. Either I'm just not simplifying it enough and the answer is correct, or I solved for λ incorrectly, or my equations are incorrect. I don't know which it is though.