Problem $2-$ Transient Analysis

The figure below provides operating data for a compressed$-$air energy storage system using off$-$peak electricity to power a compressor that fills a cavern with pressurized air $($see Sec. $4\mathrm{.}8\mathrm{.}3).$ The cavern shown in the figure has a volume of $\backslash (10^\{5\}\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ and initially holds air at $\backslash (290\backslash$mathrm$\{$~K$\},1\backslash )$ bar, which corresponds to ambient air. After filling, the air in the cavern is at $\backslash (790\backslash$mathrm$\{$~K$\},21\backslash )$ bar. Assuming ideal gas behavior for the air, determine $($a$)$ the initial and final mass of air in the cavern, each in kg $,$ and $($b$)$ the work required by the compressor, in GJ$.$ Ignore heat transfer and kinetic and potential energy effects.

Take some time to consider the assumptions of "ignore heat transfer and kinetic and potential energies" and "assume ideal gas behavior" that are given in the problem statement. Would you have made those assumptions on your own if they had not been given in the problem statement? Is the assumption of ideal gas behavior justified? Add your answers and justifications to these additional questions.