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show mathematically that work done for expansion of an ideal gas in reversible process is higher than that in irreversible process
The reversible work greater than irreversible work beacuse the key feature why the irreversible work is smaller than the reversible work is the magnitude of the external pressure against which the irreversible work is done against. If you were to increase the external pressure by a factor of two then the irreversible work would be greater. The irreversible work depends linearly on the volume and pressure whereas in the reversible work it depends logarithmically but this latest one depends linearly on the temperature. So if you want the reversible work to be less than the irreversible you have to either find a path with a low temperature for the reversible work or with high pressure for the irreversible one.
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