Question $5$

$5.$ Methane is to be compressed from $0\mathrm{.}2$ MPa and $200$ K to $10$ MPa in a two stage

compressor which operates adiabatically and reversibly. In between the two compression

stages, a heat exchanger returns the methane back to its initial temperature. The

intermediate pressure is $2$ MPa.

a$)$ What is the work required in the first stage compressor?

b$)$ What is the temperature at the exit of the first compressor?

c$)$ What is the cooling duty of the interstage cooler?

d$)$ What is the final temperature of methane?

Use the Pressure$-$Enthalpy diagram for methane provided $($on the final page of the exam

paper$),$ and clearly indicate the thermodynamic trajectories you have followed to perform

your calculations.