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Question
In a real gas, the internal energy depends on temperature and also on volume. The energy increases when the gas expands isothermally. Examining the derivation of Cp − Cv = R, find whether Cp − Cv will be more than R, less than R or equal to R for a real gas.
Solution
In a real gas, as the internal energy depends on temperature and volume, the derived equation for an ideal gas
(dQ)P = (dQ)v + nRdT will change to
(dQ)P = (dQ)v + nRdT+ k ,where k is the change in internal energy (positive) due to change in volume when pressure is kept constant. So, in the case of a real gas, for n=1 mole (say),
CP -Cv =R + `k/(dt)`
⇒ CP - Cv > R,
where Cp and Cv are the specific heat capacities at constant pressure and volume, respectively.
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