Consider a two-stage gas compressor with inter-cooling.

Assume the gas can be treated as ideal with constant specific heat. Derive an expression for the specific work input in terms of P₁ ,P₂ ,P₄ ,?₁ ,?₂ ,T₁ and T₃. Then, for all the other parameters fixed, find the value of P_2?which minimizes the work requirement. Show that, if T₃ = T₁ and ?₁ = ?₂ , the work is minimum for P₂/P₁ = ?P₄/P₁.

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W, IN 2 Intercooler 11. 2 Stage 1 7/2 Stage 2 W₂