Problem $5$: $(30$ Marks$)$ A gas turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers $32$ MW of power. The minimum and maximum temperatures in the cycle are $310$ and $900$ K$,$ and the pressure of air at the compressor exit is $8$ times the value at the compressor inlet. Assuming an isentropic efficiency of $80$ percent for the compressor and $86$ percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heat with temperature.

a$.$ Draw the Brayton cycle on a Ts diagram such that the start of the compression process is called state $1$ and so on$.$ Include both the adiabatic and isentropic compression and expansion processes. $(5$ Marks$)$

b$.$ The enthalpy at the beginning of the compression. $(2$ Marks$)$

c$.$ The isentropic enthalpy after the compression process. $(3$ Marks$)$

Note: Feel free to use an online interpolation calculator.

d$.$ The enthalpy at the end of the heat addition process. $(2$ Marks$)$

e$.$ The isentropic enthalpy after the expansion process. $(3$ Marks$)$

f$.$ Amount of the heat input. $(2$ Marks$)$

g$.$ The actual turbine work output. $(4$ Mark$)$ Ans. $\backslash (355\mathrm{.}7\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$

h$.$ The actual compressor work input. $(4$ Mark$)$ Ans. $315\mathrm{.}025$ kJ$/$kg

i$.$ Thermal efficiency of the cycle? $(2$ Marks$)$

j$.$ The mass flow rate of the air? $(3$ Marks$)$ Ans: $\backslash (786\mathrm{.}6\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$