## Constant pressure/volume

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### Constant pressure/volume

What exactly does Cp=5/2*R and Cv= 3/2*R mean? When would we use it?

Vincent Tse 1K
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### Re: Constant pressure/volume

Cv = 3/2 * R is the relationship that you derive for monoatomic gases. Cv is the heat capacity at a constant volume.

The derivation involves using ΔE = (3/2)nRΔT (for monoatomic gases) and the first law of thermodynamics, Q = ΔE + W.
W is 0 at constant volume, so you plug in ΔE on the right, the substitute the Q on the left with Q=nCvΔT. The n's and ΔT's cancel, leaving you with that relationship.

Cp = 5/2 * R is the same idea but at constant pressure instead of volume, so W is not zero (it's equal to PΔV, which in turn is equal to nRΔT).

You use these when dealing with monoatomic ideal gases...diatomic/polyatomic ones have different properties!

Wayland Leung
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### Re: Constant pressure/volume

When would we need to use these values of 5/2R and 3/2R? Could you give some context?