Answer to Question #250022 in Electrical Engineering for Mangi

Question #250022

Derive the isentropic relation of state.


1
Expert's answer
2021-10-13T02:54:01-0400

For a closed system, the total change in energy of a system is the sum of the work done and the heat added:

"dU=dW+dQ\\\\\ndW=-pdV\\\\\ndH=dU+pdV+Vdp\\\\\ndU=dW+dQ= -pdV+0\\\\\n\\implies dU=nC_vdT\\\\\n\\implies dH=nC_pdT\\\\\ndU=nC_vdT=-pdV\\\\\ndH=nC_pdT=-Vdp\\\\\n\\implies \\gamma= \\frac{C_p}{C_v}= \\frac{dp\/p}{dV\/V}\\\\\nHence \\space \\frac{p_2}{p_1}= (\\frac{V_1}{V_2})^{\\gamma}\\\\"


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