HW $-12$

A closed, externally well$-$insulated rigid tank is divided into two sections by a partition. Initially one section

contains $2$ kg of air at an absolute pressure of $5$ bar and an absolute temperature of $350$ K while the other

section contains $4$ kg of carbon dioxide gas at an absolute pressure of $2$ bar and an absolute temperature of

$450$ K $($State $1).$ The partition is free to move and allows heat transfer between the two gases until

mechanical and thermal equilibrium is achieved $($State $2).$ Assume constant specific heats for both gases

and that the partition has negligible volume.

For air:

Molecular weight $=28\mathrm{.}97k\frac{g}{k}$mol; Specific heat at constant pressure $c_p=1\mathrm{.}005k\frac{J}{k}g-K$

For carbon dioxide:

Molecular weight $=44\mathrm{.}01k\frac{g}{k}$mol; Specific heat at constant pressure $c_p=0\mathrm{.}977k\frac{J}{k}g-K$

$($a$)$ Calculate the absolute temperature at equilibrium, in K $.$

$($b$)$ Determine the absolute pressure at equilibrium, in bar.

$($c$)$ Find the volume of each gas at equilibrium, in $m^3.$