Question

Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pv^k = constant, where k is the isentropic expansion exponent defined as k = -v/P (∂P/∂v). Also, show that the isentropic expansion exponent k reduces to the specific heat ratio cp/cv for an ideal gas.

Name: consider an infinitesimal reversible adiabatic compression or expansion process by taking s sp v and using the maxwell relations show that for this process pvk constant where k is the isentr 70567
Uploaded: 2022-06-15T09:00:34-08:00
Duration: 3 min 4 s
Channel: Adriano Chikande
Description: consider an infinitesimal reversible adiabatic compression or expansion process by taking s sp v and using the maxwell relations show that for this process pvk constant where k is the isentr 70567

          Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pv^k = constant, where k is the isentropic expansion exponent defined as k = -v/P (∂P/∂v). Also, show that the isentropic expansion exponent k reduces to the specific heat ratio cp/cv for an ideal gas.

Added by Deanna M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adriano Chikande

06/15/2022

Step 1

They relate the partial derivatives of the thermodynamic potentials. For a system described by the entropy s, pressure P, and specific volume v, the relevant Maxwell relation is: (∂s/∂v)_P = -(∂P/∂T)_v Show more…

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Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pv^k = constant, where k is the isentropic expansion exponent defined as k = -v/P (∂P/∂v). Also, show that the isentropic expansion exponent k reduces to the specific heat ratio cp/cv for an ideal gas.