In a Brayton cycle gas turbine power plant the minimum and maximum temperatures of the cycle are 300 K and 1200 K. The compression is carried out in two stage of equal pressure ratio with intercooling of the working fluid to the minimum temperature of the cycle after the first stage of compression. The entire expansion is carried out in one stage only. The isentropic efficiency of both compressors is 0.85 and that of the turbine is 0.9. Determine the overall pressure ratio that would give the maximum net work per kg working fluid. Derive the expression you use $\gamma$ = 1.4