$(34\%)$ An air compressor and regenerative heat exchanger for a gas turbine system operate at steady state. Air flows from the compressor through the regenerator, a separate stream of air passes through the regenerator in a counter flow arrangement. Operating data are provided below. Heat transfer to the surroundings can be neglected. The compressor power input is $6700$ kW $.$ Assume the air to have constant specific heat evaluated at $300$ K $.$ Determine:

a$)$ The mass flow rate of air entering the compressor $(k\frac{g}{s}).$

b$)$ The compressor isentropic efficiency.

c$)$ The temperature of the air exiting the regenerator at state $5(k).$

d$)$ The rate of entropy generation for the compressor only $(k\frac{J}{s}K).$