The work during that process can be expressed as
W=n−1pbVb−paVa. According to the first law of thermodynamics, for a gas with degrees of freedom of molecules i we can write:
Q=ΔU+W=2iμmRΔT+n−1pbVb−paVa. Since
pV=μmRT, we can now write that
Q=ΔU+W=2iμmRΔT+n−1μmRΔT= =μmRΔT(2i+n−11)=μmRΔT⋅2(n−1)in−i+2.
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