Consider an idcal gas of n moles with molar specific heats cy and cp. (a) Starting with the first law, show that when the temperature and volume of this gas are changed by a reversible process, its change in entropy is given by dT dV + nR- T dS = ncv (b) Show that the expression in part (a) can be written as dP + nCP dS = AP псу (c) Using the cxpression from part (b), show that if dS = 0 for the reversible process (that is, the process is adiabatic), then PVY = constant, where y = cp/cv.

Consider an idcal gas of n moles with molar specific heats cy and cp. (a) Starting with the first law, show that when the temperature and volume of this gas are changed by a reversible process, its change in entropy is given by dT dV + nR- T dS = ncv (b) Show that the expression in part (a) can be written as dP + nCP dS = AP псу (c) Using the cxpression from part (b), show that if dS = 0 for the reversible process (that is, the process is adiabatic), then PVY = constant, where y = cp/cv.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter18: Heat Engines, Entropy, And The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 34P

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