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For two moles of an ideal gas(Cy -Cp)--2R,\begin{array}{l}{\text { (a) }\left(G_{V}-C_{p}\right)=-2 R} \\ {\text { (c) }\left(C_{p}-C_{V}\right)=R}\end{array} |
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Answer» Cp - Cv = RThis is a standard relation for one mole. For two moles the difference will be = 2 R. In general Cp - Cv = n R ---- (0)============We know PV = n R T, V = (nR/P) * T --- (1) At constant pressure, ΔV/ΔT = nR/P --- (2) From first law of thermodynamics, we have that ΔQ =ΔU + W =ΔU + PΔV ---- (3)We know that the internal energy U and the change in it ΔU, are entirely dependent on the temperaturefor the same amount of substance. So it does not depend on the pressure or volume. Cp = [ ΔQ/ΔT ]_P=const = [ ΔU/ΔT ]_P=const + P * [ ΔV/ΔT ]_P=const = ΔU/ΔT + P * n R/P =ΔU/ΔT + n R Cv = [ΔQ/ΔT ]_V=const = [ΔU/ΔT ]_V=const + P [ ΔV/ΔT ]_V=const =ΔU/ΔT + 0 Hence Cp = Cv + n R Cp-Cv=2R in book correct answer is c |
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