P$2.$

The below figure 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. The cavern shown in the figure has a volume of ${10}^5{m}^3$ and initially holds air at $290K,\frac{1}{b}ar,$ which corresponds to ambient air. After filling, the air in the cavern is at $790K,21$ bar. Assuming ideal gas behaviour 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 energy transfer due to heat interaction and kinetic and potential energy effects.

Air at $290K,1$ bar