Air with a mass flow rate of $0\mathrm{.}2$ kg$/$s is compressed from $100$ kPa pressure and $20\backslash$deg Ctemperature to $500$ kPa pressure and $170\backslash$deg C in a compressor. The compressor requires $40$ kW power.

a$)$ Find the heat transferred from the compressor to the surrounding air at $17\backslash$deg C$.$

b$)$ Calculate the entropy production per unit time.

c$)$ The energy required for the compressor is provided by an adiabatic $($no heat loss$)$ steam turbine. Steam enters the turbine at $4$ MPa pressure and $500\backslash$deg C temperature and leaves at a pressure of $0\mathrm{.}5$ bar and $0\mathrm{.}92$ quality. Calculate the mass flow rate of steam required.Kinetic and potential energy changes can be neglected.