Determine the work required to compress $10$ kg of an ideal gas, molecular weight $28$ kg$/$kmol from $10$ kP to $100$ kPa. The isentropic compression is accomplished in a two stage compressor. The gas enters the first stage at $200$ K and if the mechanical efficiency of the compressor is $0\mathrm{.}85.$ Also, calculate the temperature of the gas leaving the first stage assuming that the compression ratio is the same in both stages. R$0=8\mathrm{.}314$ kJ$/$kmol K$,$ Y $=1\mathrm{.}4$