Problem $2(16$ points$)$

A propane supplier is designing an industrial system to liquefy gaseous propane. Propane $($mass flow rate of $10k\frac{g}{s})$ enters a chiller $($a type of heat exchanger$)$ at a quality of $90\%$ and pressure of $100$ kPa and exits as a saturated liquid. The ambient environment $($the high temperature reservoir for the process$)$ is at $300$ K $.$

a$)$ How much heat must be removed from the propane, in kW$,$ to liquefy it$?(5$ points$)$

b$)$ Sketch the process on a p$-$v diagram, including the vapor dome. $(2$ points$)$

c$)$ What is the minimum work input, in kW $,$ to the refrigeration cycle connected to the chiller? $(7$ points$)$

Hint: It may be helpful to reduce this to a cycle diagram operating between two reservoirs $($as for the refrigeration example in lecture$)$

d$)$ How much heat is rejected to the ambient environment, in kW$?(2$ points$)$