PART C $(35$ pts$)$: During a high$-$stakes race, a race car uses steam$-$driven nozzles to improve aerodynamic control and boost its performance. In one of the nozzles, steam enters as a saturated vapor of $6$MPa with a negligible inlet velocity and expands to a pressure of $1\mathrm{.}2$ MPa.

a$)(5$ pts $)$: Identify and explain the key assumptions that can be made to simplify the analysis of this nozzle's operation. Consider factors such as the type of process, the system's flow conditions, and any relevant simplifying assumptions that would be reasonable in this race car application. Justify how these assumptions influence the system process type and the energy balance equation.

b$)(10pts)$ : Write the energy balance equation for the system. Clearly state which terms are neglected due to the assumptions you identified in $($a$).$ How does this equation reflect the First

Law of Thermodynamics?

c$)(10$ pts$)$: Sketch the T$-$s diagram for this process with respect to the saturation lines, assuming the nozzle achieves the maximum possible exit velocity. Indicate the states of the steam at the nozzle's inlet and outlet, and clearly label relevant lines and points.

d$)(2\mathrm{.}5$ pts $)$: Discuss how the assumptions and energy balance equation you developed in $($b$)$ reflect the application of the First Law of Thermodynamics.

e$)(2\mathrm{.}5$ pts $)$: Which assumptions and analysis reflect considerations from the Second Law of Thermodynamics? Discuss briefly.

f$)(5$ pts $)$: Determine the maximum exit velocity of the steam in $\frac{m}{s}.$ Provide a clear step$-$by step solution and indicate where the assumptions and equations derived in earlier parts of the problem are used.