Consider an ideal gas of n moles with molar specificheats

Chapter 20, Problem 20.51

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Consider an ideal gas of n moles with molar specificheats Cy and CP. (a) Starting with the first law, show thatwhen the temperature and volume of this gas are changedby a reversible process, its change in entropy is given bydS = nC^ ydT + nR-d^Vr-(b) Show that the expression in part (a) can be written as^ dP dVdS nCy p + nCp y '(c) Using the expression from part (b), show that if dS = 0for the reversible process (that is, the process is adiabatic),then PVy = constant, where J = CP/CV.

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