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Reversible adiabatic expansion proof
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[QUOTE="Latsabb, post: 4990044, member: 468489"] [h2]Homework Statement [/h2] 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^[SUP][/SUP](C[SUB]p,m[/SUB]/R)/P = constant Where R is the gas constant and C[SUB]p,m[/SUB] is the molar heat capacity. [h2]Homework Equations[/h2] ΔU=Q-W pV=nRT Possibly relevant: W[SUB]rev[/SUB]=-pdV γ=C[SUB]p,m[/SUB]/C[SUB]v,m[/SUB] where γ is the heat capacity ratio. PV[SUP]γ[/SUP]= constant [h2]The Attempt at a Solution[/h2] 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[SUP]γ[/SUP] into some relation for T to the power of some derivative of gamma. I assume since gamma has C[SUB]p,m[/SUB] 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. [/QUOTE]
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Reversible adiabatic expansion proof
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