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## Homework Statement

Prove the relationship between the pressure, P, and the temperature, T, for an ideal gas with a reversible adiabatic expansion. Base the proof on the first law of thermodynamics and the ideal gas law.

The relationship is: T^(C

_{p,m}/R)/P = constant

Where R is the gas constant and C

_{p,m}is the molar heat capacity.

## Homework Equations

ΔU=Q-W

pV=nRT

Possibly relevant:

W

_{rev}=-pdV

γ=C

_{p,m}/C

_{v,m}where γ is the heat capacity ratio.

PV

^{γ}= constant

## The Attempt at a Solution

I don't even know where to start explaining what I have tried... I have been kicking around a lot of things. I can't seem to manage to manipulate things so that temperature is to the power of anything, although I have burnt a lot of time trying to turn PV

^{γ}into some relation for T to the power of some derivative of gamma. I assume since gamma has C

_{p,m}in it, that it is going to play in, and especially since it is already a power for volume, this flagged me in that direction, but I am just going around in circles.

Any help in the right direction would be GREATLY appreciated.