$5\mathrm{.}1$ A basic air$-$standard gas turbine engine has a compressor inlet temperature of $519$R $(288$K$)$ and a turbine inlet temperature of $2160$R $(1200$K$).$ Calculate, assuming constant specific heats:

a$)$ The pressure ratio that gives the maximum net work.

b$)$ The compressor work, turbine work, heat added, and thermal efficiency corresponding to the pressure ratio in part a$).$

$5\mathrm{.}2$ Solve Problem $5\mathrm{.}1$ assuming variable specific heats and a pressure ratio of $8.$ Compare the net work and thermal efficiency with the values $$determined in Problem $5\mathrm{.}1$