Figure $1$ shows a block diagram for the Claude process that is used to liquify methane. The Claude process serves as an example to comprehensively synthesize all the concepts taught from week $1$ to week $6$ of $CH2123.$ Fresh methane $($stream $1)$ is combined with recycled methane $($stream $19)$ and then compressed $,$ and $C3$ to

$80$ bar. Intercoolers $($HE$1,$ HE$2,$ and HE$3)$ after each compressor remove heat from the incoming gas. The compressed methane is then further cooled in heat exchangers HE$4$ and HE$5$ before being throttled. The flash drum operates at $1$ bar. Liquid methane exits

the flash drum in stream $13($saturated liquid, $1$ bar$).$ A draw$-$off stream $($stream $15,0\mathrm{.}30k\frac{g}{s})$ is passed through an expander $($E$1)$ before combining with the un$-$liquified methane stream $($stream $14,$ saturated vapour at $1$ bar$)$ and is then recycled back $($streams $17,18,$

and $19).$ The draw$-$off stream leaves the expander as a saturated vapour at $1$ bar. Table $1$ contains the temperature, pressure, specific enthalpy, and specific entropy of all streams. Selected mass flow rates are also provided. All compressors and expanders are adiabatic. Assume all processes to be at steady state. Neglect the kinetic and potential energy terms. a$.$ Determine whether the compressors $C1,C2,$ and $C3$ and the expander $E1,$ are reversible or irreversible.Figure $1$: C$,$ E$,$ and HE signify compressor, expander, and heat exchanger respectively.

W and $Q$ represent work and heat terms with the arrows indicating whether they are

added to the system, or removed from the system.

Table $1$: Thermodynamic properties and mass flow rates of streams shown in Figure $1.$

b$.$ Calculate the work inputs to compressors $C1,C2,$ and $C3,$ and the work obtained from expander $E1$ in units of $k\frac{J}{s}.$

c$.$ Determine the efficiency of the expander E$1.$ The exhaust from the expander is saturated vapour at $1$ bar $($stream $16).$

d$.$ Calculate the mass flow rate $(k\frac{g}{s})$ of liquified methane exiting the system $($stream $13).$