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^(Cp,m/R)/P = constant
Where R is the gas constant and Cp,m is the molar heat capacity.
γ=Cp,m/Cv,m where γ is the heat capacity ratio.
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 PVγ into some relation for T to the power of some derivative of gamma. I assume since gamma has Cp,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.