Investigate the optimal pressure, P₂, for a constant-pressure intercooler between two stages in a compressor. Assume that the compression process in each stage follows a poly tropic process and that the intercooler brings the substance to the original inlet temperature, T1. Show that the minimal work for the combined stages arises when P₂ = (P₁P₃)^1/2 where P₃ is the final exit pressure.