Problem $5(10$ points$)-$ Entropy generation rate analysis

The figure below shows an air compressor and regenerative heat exchanger in a gas turbine system operating at steady state. Air flows from the compressor through the regenerator, and a separate stream of air passes through the regenerator in counterflow. Operating data are provided in the figure. Stray heat transfer to the surroundings and kinetic and potential energy effects can be neglected. The compressor power input is $6700$ kW $.$ Using the method of variable specific heats and assuming that the surroundings temperature is $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ please answer the following.

a$.$ Determine the mass flow rate of air entering the compressor, in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$

b$.$ Calculate the temperature of the air exiting the regenerator at state $(5),$ in K$.$

c$.$ Compute the rates of entropy generation in the compressor and regenerator separately, in kW$/$K$.$

d$.$ Using a control volume that includes both the regenerator and compressor and neglecting any irreversibility and heat transfer in the lines connecting the compressor to the regenerator, set the equation to compute the total entropy generation rate and perform the computation, in kW$/$K$.$ Is your result equal to the sum of the entropy generated by the compressor and heat exchanger? Why?

e$.$ Based on the assumptions used in the solution of parts $($c$)$ and $($d$),$ are the processes shown for the compressor and heat exchanger feasible? Why?