Question $2(15$ marks$)$

Methane is liquefied in a simple Linde system, as shown in Figure. The methane enters the compressor at $1$ bar and $300K,$ and after compression to $60$ bar it is cooled back to $300K.$ The product is saturated liquid methane at $1$ bar. The unliquefied methane,$1$bar returned through a heat exchanger, where it is heated to $295K$ by the high$-$pressure methane. Make a thermodynamic analysis of the process for i$$eal work equal to $1053\mathrm{.}8kJ.$

Data used here is from Perry and Green. The basis of all calculations is $1kg$ of methane entering the process, and all rates are expressed on this basis.

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