Maximum allowable working pressure $($MAWP$)$ is a designation set by the American Society of Mechanical Engineers $($ASME$).$ The MAWP is the greatest amount of pressure

that the weakest part of the vessel can handle at specific operating conditions. When a vessel is designed, calculations are completed using the range of operating conditions

$($with allowances on each side of the range$),$ construction materials, and vessel type$/$construction$,$ to determine the MAWP and thus the rating for the pressure$-$relief

components. MAWPs are given in equipment specifications and are used to set safety protocols to ensure that the system never exceeds safe operating pressures.

A tank $(10$ in diameter and $32$ in height$)$ at $77F$ is charged with pure nitrogen. An engineer used the ideal$-$gas equation of state to determine that the MAWP would be

reached if the tank is charged with $50$ pounds of nitrogen.

a$.(5$ points$)$ The MAWP is

psig. Answer to the nearest integer.

b$.(15$ points$)$ Using the compressibility chart, the pressure is

psig. Answer to the nearest integer. Your work must be documented on the chart.

c$.(10$ points$)$ Using the Peng$-$Robinson equation of state the pressure is

psig. Answer to the nearest integer.

d$.(5$ points$)$ Would you recommend using the ideal gas equation of state?

Why or why not?

please output all steps with integer values.