Air enters the compressor of a simple gas turbine at $p_1=14$ psia,$T_1=500R.$ The isentropic efficiencies of the compressor and turbine are $82$ and $90\%,$ respectively. The compressor pressure ratio is $10$ and the temperature at the turbine inlet is $2950R.$ The net power developed is $4\mathrm{.}5{10}^{6}Bt\frac{u}{h}.$ On the basis of an air$-$standard analysis, calculate:

a$)$ the volumetric flow rate of the air entering the compressor, in $f\frac{t^3}{m}in.$

b$)$ the temperatures at the compressor exit, in $R.$

c$)$ the temperatures at the turbine ecit, in $R.$

d$)$ the thermal efficiency of the cycle.