Constant pressure/volume
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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!
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!
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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?
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