$4.(25$ points$)$

An A simple Brayton cycle delivers $50$ MW of power using air as a working fluid. The low temperature in the cycle is $300$ K and the high temperature of the cycle is $1000$ K $.$ The compressor has a compression ratio of $8$ to $1.$ Accout for the variability of heat capacity with temperature $($do not assume constant heat capacities$).$

a$)(5$ points$)$ sketch a TS diagram of the cycle and for each process indicate the direction of heat or work flow

b$)$ determine the mas flow rate of air in the system

c$)$ what is the thermal efficiency of this system

Now assume a $\backslash (90\backslash \%\backslash )$ isentropic efficiency for the turbine and an $\backslash (85\backslash \%\backslash )$ isentropic efficiency for compressor.

d$)$ what is the new mass flow rate of air in the system assuming the $50$ MW power output is maintained with the less efficient compressor and turbine assumptions

e$)$ what is new thermal efficiency of this system with the less efficient compressor and turbine assumptions