A two$-$stage compressor receives $0\mathrm{.}50$ kg$/$s of helium at $135$ kPaa and $27$ oC$,$ and

delivers it at $7000$ kPaa. The compression is polytropic with n $=1\mathrm{.}5.$ The intercooler is ideal.

Determine a$)$ the power required; b$)$ the intercooler pressure; c$)$ the maximum temperature;

d$)$ the temperature for one stage of compression; and e$)$ the heat transferred in the

intercooler. Note: For helium gas, R $=2\mathrm{.}077$ kJ$/$kgoK and k $=1\mathrm{.}666.$