A tank containing $C{O}_2$ initially at $400K$ and $50$ bar is vented until the temperature drops to $300K.$ There is no heat transfer between the gas and the tank or between the tank and the surroundings. Find the final pressure in the tank and the fraction of the initial mass of $C{O}_2$ that remains in the tank for the following cases.

a$.$ the EOS is $P(V_{-}b)=RT$ with $b=0\mathrm{.}0441\frac{m^3}{m}ol($ANS: $\frac{12\mathrm{.}9}{b}ar,36\%$ remains$)$

b$.$ the principle of corresponding states $($ANS: $15$ bar, $23\%$ remains$)$

c$.$ the Peng$-$Robinson equation of state $($ANS: $14\mathrm{.}6$ bar, $38\%$ remains$)$

d$.$ using thermodynamic property data for $C{O}_2($ANS: $13\mathrm{.}5$ bar, $31\%$ remains$)$