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Define Entropy of Ideal Gas?
A vessel of volume V1 contains N molecules of an ideal gas held at temperature T and pressure P1. The energy of a molecule may be written in the form
Where ?k denotes the energy levels corresponding to the internal states of the molecules of the gas.
a) Calculate the free energy F. Explicitly display the dependence on the volume V1.
At this time consider another vessel, as well at temperature ?? containing the same number of molecules of the identical gas held at pressure P2.
b) Give an phrase for the total entropy of the two gases in terms of P1, P2, ??, N.
c) The vessels are then connected to allow the gases to mix without doing work. Calculate explicitly the change in entropy of the system. Ensure whether your answer makes sense by considering the special case V1=V2 (P1 =P2).
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