II$.$ In this problem, we are going to analyze the gas$-$turbine engine that operates on an ideal Brayton cycle. For this, we will consider the following conditions:

The compressor is adiabatic and reversible.

The combustor operates at constant pressure condition.

The carbine is adiabatic and reversible.

The nozale expands the exhaust gas to a final exit pressure that is equal to the inlet pressure of the compressor.

Worki

Assum $$

Answer the following questions:

$($a$)$ Sketch a schematic of this cycle.

$($b$)$ Draw a P$-$v diagram for this cycle. Label all thermodynamic processes in the diagram $($using key words: compression, expansion, and combustion$),$ and indicate all states as

$1$: inlet to compressor

$2$: outlet compressor

$3$: outlet to constant pressure combustor

$4$: downstream exit of the turbine

$($c$)$ Draw a T$-$s diagram for this cycle. Use the same notation as above to label all thermodynamic processes and states.

$($d$)$ Let $P_1=80$kPa,$T_1=300K,$ the pressure ratio $\frac{P_2}{P_1}=20,$ and the heat added in combustor is $1,000kJ$ per kilogram of air. Calculate the maximum temperature in the amain $-m-m.$

$($ife$)$ Compute the work that is necessary to drive the compressor. $J$

$($f$)$ Calculate the specific entropy change in the combustor.

$($g$)$ Compute the temperature at the exit of the turbine, state $4.$

$($b$)$ What is the entropy change in the compressor?