At moderate pressures, methane obeys the following equation of state:

$Z=1+\frac{BP}{RT}$

With $B=a-\frac{b}{RT}$ and $a=4\mathrm{.}3{10}^{-5}\frac{m^3}{m}ol,b=2\mathrm{.}29\frac{{10}^{-6}}{b}ar\frac{m^6}{m}o{l}^2.$ At very low

pressures, methane heat capacity obeys $C_P=+T$ with $=19\mathrm{.}87k\frac{J}{\text{K}\text{k}\text{m}\text{o}\text{l}}$ and $=0\mathrm{.}05$

$k\frac{J}{K^2\text{k}\text{m}\text{o}\text{l}}.$

a$)$ Compute the adiabatic power required to compress $2$kmo$\frac{l}{s}$ of methane from $290K,5$

bar to $450K,22$ bar.

Determine the rate of entropy generation from this process.

b$)$ Compare your answers to values calculated when ideal gas behavior is assumed.