$(50$ points$)$ A closed cylindrical tank $($large vessel$)$ of known dimensions $(L=1m$ and $d=0\mathrm{.}15m)$ contains $5$ Kg of colorless carbon monoxide $($CO$)$ gas at $-50C.$ Evaluate the pressure exerted by the CO gas using $($a$)$ the ideal gas equation of state, $($b$)$ the generalized compressibility equation and $($c$)$ the Van der Waals equation. Calculate the average percent error on the pressure using the following equation

Error $=(100\%)\frac{P_{\text{r}\text{e}\text{a}\text{l}}-P_{\text{i}\text{d}\text{e}\text{n}\text{l}}}{P_{\text{r}\text{e}\text{a}\text{l}}}$

Available data set and compressibility chart.

$M=28\mathrm{.}011K\frac{g}{k}$mol,$R=0\mathrm{.}2968k.\frac{J}{K}g.K,T=-50+273K=223K$

$($a$)1\mathrm{.}1$ The ideal equation of state $($EOS$)$ yields the pressure as

a$,P=11\mathrm{.}06$MPa

b$.P=11\mathrm{.}06$kPa

c$.P=23\mathrm{.}57$MPa

d$.$ None of the above

$($b$)1\mathrm{.}2$ From the generalized compressibility chart, verify that $v_r=0\mathrm{.}31$ by marking a visible dot on it

a$.$ Done correctly

b$.$ Done incorrectly

$1\mathrm{.}3$ From the compressibility chart, the corresponding pressure is

a$.P=10\mathrm{.}82$MPa

b$.P=21\mathrm{.}34$kPa

c$.P=18\mathrm{.}90$MPa

d$.$ None of the above

$1\mathrm{.}4$ Using the compressibility equation yields the pressure as

a$.P=16\mathrm{.}89$MPa

b$.P=14\mathrm{.}23$kPa

c$.P=11\mathrm{.}58$MPa

d$.$ None of the above

$1\mathrm{.}5$ The compressibility average pressure value is

a$.P=17\mathrm{.}90$MPa

b$.P=11\mathrm{.}56$kPa

c$.P=15\mathrm{.}69$MPa

d$.$ None of the above

$1\mathrm{.}6$ The percent pressure error related to the average pressure

a$.$ error $=38\mathrm{.}21\%$

b$.$ error $=18\mathrm{.}65\%$

c$.$ error $=12\mathrm{.}77\%$

d$.$ None of the above

$($c$)1\mathrm{.}7$ Using the Van der Waals equation, the pressure is

a$.P=17\mathrm{.}37$MPa

b$.P=18\mathrm{.}43$kPa

c$.P=16\mathrm{.}45$MPa

d$.$ None of the above

$1\mathrm{.}8$ The percent pressure error related to the average pressure

a$.$ error $=36\mathrm{.}33\%$

b$.$ error $=25\mathrm{.}67\%$

c$.$ error $=15\mathrm{.}43\%$

d$.$ None of the above

$1\mathrm{.}9$ The carbon monoxide $($CO$)$ gas at $T=-50C$ deviates significantly from ideal gas behavior.

a$.$ True

b$.$ False

$1\mathrm{.}10$ At a temperature of $223$ K $,$ carbon monoxide $($CO$)$ gas deviates from ideal gas behavior primarily due to effects of intermolecular forces and the finite volume of gas molecules.

a$.$ True

b$.$ False

$(50$ points$)$ A closed cylindrical tank $($large vessel$)$ of known dimensions $(L=1m$ and $d=0\mathrm{.}15m)$ contains $5$ Kg of colorless carbon monoxide $($CO$)$ gas at $-50C.$ Evaluate the pressure exerted by the CO gas using $($a$)$ the ideal gas equation of state, $($b$)$ the generalized compressibility equation and $($c$)$ the Van der Waals equation. Calculate the average percent error on the pressure using the following equation

Error $=(100\%)\frac{P_{\text{r}\text{e}\text{a}\text{l}}-P_{\text{i}\text{d}\text{e}\text{a}\text{l}}}{P_{\text{r}\text{e}\text{a}\text{l}}}$

Available data set and compressibility chart.

$M=28\mathrm{.}011K\frac{g}{k}$mol,$R=0\mathrm{.}2968k.\frac{J}{K}g.K,T=-50+273K=223K$

$T_{-}=-150C-133K,P_r=3\mathrm{.}50$MPa,$r_r=0\mathrm{.}0930\frac{m^3}{K}g$