To do testing at representative geothermal conditions $(250$C and $690$ bar$),$ we have a small uninsulated pressure vessel. In preparation for a particular test, we were pressurizing the vessel using an air compressor. Unfortunately, the pressure vessel had a faulty relief valve that was causing it to vent to atmosphere $(25$C and $1$ bar$)$ when the pressure vessel was at $10$ bar, however, we were unaware of this

and continued pumping air into the pressure vessel at $10$ L$/$s $($entrance to the vessel$).$ After some time, the temperature in the pressure vessel reached $100$C and remained constant. Assuming that we are at steady state and the air leaking from the tank equilibrates with the ambient$/$atmosphere at a small distance

from the outlet of the valve, answer the following:

$($a$)$ Sketch the system and energy flow described in this problem statement.

$($b$)$ What is the power required by the compressor? You may assume that the compressor has anisentropic efficiency of $80\%.$

$($c$)$ What is the temperature of air at the outlet of the compressor $($before it gets to the tank$)?$

$($d$)$ What is the rate of entropy generation for the compressor?

$($e$)$ What is the total rate of entropy generation $($hint$,$ draw a control volume around all components$)?$

$($f$)$ Describe in words, the sources of entropy generation for part $($e$)?$