HW$\backslash$#$5$

P$1.$ Use the enthalpy data $($miniREFPROP$)$ to calculate the fraction of nitrogen liquefied on each pass through a Hampson$-$Linde cycle operating between $1$ bar and $100$ bars, with an input temperature of $300$ K $.$ Assume that the heat exchanger works perfectly, so the temperature of the gas coming out of it is the same as the temperature of the high$-$pressure gas going in $($Compressor works isothermally, $\backslash (\backslash$mathrm$\{$T$\}2=\backslash$mathrm$\{$T$\}1\backslash ))$

Find compressor work per unit mass liquefied at this temperature.

Using $($miniREFPROP$)$;

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}$

$\backslash$hline State & $1$ & $2$ & f $\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$atm$\})\backslash )$ & $1$ & $100$ & $1\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathrm$\{$~T$\}(\backslash$mathrm$\{$~K$\})\backslash )$ & $300$ & $300$ & $77\mathrm{.}34\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathrm$\{$~h$\}(\backslash$mathrm$\{$KJ$\}/\backslash$mathrm$\{$Kg$\})\backslash )$ & $311\mathrm{.}19$ & $291\mathrm{.}72$ & $-122\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathrm$\{$~s$\}(\backslash$mathrm$\{$KJ$\}/\backslash$mathrm$\{$Kg$\}\backslash$mathrm$\{$K$\})\backslash )$ & $6\mathrm{.}84$ & $5\mathrm{.}41$ & $2\mathrm{.}83\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$