A common problem in the design of chemical processes is the steady-state compression of gases from a low pressure P₁ to a much higher pressure P₂. We can gain some insight about optimal design of this process by considering adiabatic reversible compression of ideal gases with stage-wise intercooling. If the compression is to be done in two stages, first compressing the gas from P₁ to P*, then cooling the gas at constant pressure down to the compressor inlet temperature T₁, and then compressing the gas to P₂, what should the value of the intermediate pressure be to accomplish the compression with minimum work?

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