Problem $10\mathrm{.}092-$ Air flow rate in variable heat capacity Brayton Cycle..

A gas$-$turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers $31\mathrm{.}00$ MW of power. The minimum and maximum temperatures in the cycle are $310$ and $900$ K $,$ and the pressure of air at the compressor exit is $8$ times the value at the compressor inlet. Assuming an isentropic efficiency of $80$ percent for the compressor and $86$ percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.

The mass flow rate of air through the cycle is $k\frac{g}{s}.$