Problem $5(10$ points$)$

Air at a mass flow rate of $5400k\frac{g}{h}$ and $325$ K enters a heater and leaves at $1020$ K as shown in the figure below. This hot air then enters a turbine where it expands to generate $204$ kW of work. Assuming variable specific heats, calculate the following for the heater$-$turbine system:

a$)$ The heat supplied to the heater, $Q_1^{}.$

b$)$ The air temperature at the outlet of the turbine, $T_3.$

Now assume that the air at the outlet of the turbine is connected to an insulated air tank through a valve. Calculate the following for this modified system:

a$)$ The temperature of the air at state $4($in the tank$).$

b$)$ Discuss what happens to the temperature at state $4$ as the air in the tank is pressurized.

$($Hint: what is the difference between a moving and a stationary fluid?$)$