HW $-13$

Carbon dioxide $(m=2kg)$ contained inside a closed piston$-$cylinder device undergoes three processes.

Consider carbon dioxide as an ideal gas with variable properties with temperature.

Molecular weight of carbon dioxide $=44\mathrm{.}01k\frac{g}{k}$mol

Process $1$ to $2$: A constant volume process from an absolute pressure of $1$ bar and an absolute temperature

of $300$ K $($State $1)$ to an absolute pressure of $4$ bar $($State $2)$

Process $2$ to $3$: A polytropic process $P{v}^{1\mathrm{.}28}=$ constant to an absolute pressure of $1$ bar $($State $3)$

Process $3$ to $1$: A constant pressure process

$($a$)$ Calculate the volume at State $1$ and State $3,$ each in $m^3.$

$($b$)$ Determine the temperature at State $2$ and State $3,$ each in K $.$

$($c$)$ Find the work for each process, in kJ $.$

$($d$)$ Calculate the heat transfer for each process, in kJ$.$

$($e$)$ Show the three processes on $P-V$ diagram and the appropriate lines of constant temperature for the three

states. Label states and identify process directions with arrows.