Problem $6(20$ points$)$

A small rigid cylindrical tank contains $38$ grams of carbon dioxide at $31C$ and $8797$ kPa $.$ The rigid tank and the carbon dioxide contained within are now slowly heated until it bursts at a pressure of $31,735$kPa.

Assuming real gas behavior in all cases $-$

at State $1,$ determine: a$)$ compressibility factor using EES or the compressibility chart and Table A$-1$;

b$)$ the specific volume of the tank $(\frac{m^3}{k}g)$; and c$)$ the volume of the tank $(c{m}^3).$

Mark State $1$ on the compressibility chart included with the problem.

at State $2,$ estimate: d$)$ the temperature of the carbon dioxide in the tank just before it bursts $(C)$; and e$)$ the boundary work during the heating process $($ kJ $).$

Assuming a factor of safety of $2$ for the safe operating pressure $($i$.$e$.,\frac{P_{\text{b}\text{u}\text{r}\text{s}\text{t}}}{2}),$ determine: $f)$ the safe operating pressure $($ kPa $)$; and g$)$ the maximum recommended safe operating temperature $(C).$

Note EES is recommended versus chart iteration.