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Chemistry LibreTexts

19.5: The Temperature of a Gas Decreases in a Reversible Adiabatic Expansion

We can make the same argument for the heat along C. If we do the three processes A and B+C only to a tiny extent we can write:

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And now we can integrate from V1 to V2 over the reversible adiabatic work along B and from T1 to T2 for the reversible isochoric heat along C. To separate the variables we do need to bring the temperature to the right side of the equation.:

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The latter expression is valid for a reversible adiabatic expansion of a monatomic ideal gas (say Argon) because we used the Cv expression for such a system. We can use the gas law PV=nRT to translate this expression in one that relates pressure and volume see Eq 19.23