An insulated piston$/$cylinder initially contains R$-22$ at $20\backslash$deg C$,85\%$ quality, at a cylinder volume

of $50$ L$.$ A valve at the closed end of the cylinder is connected to a line flowing R$-22$ at $1$ MPa,

$60\backslash$deg C$.$ The valve is opened, allowing R$-22$ to flow in$,$ and at the same time the external force on

the piston is decreased, and the piston moves. When the valve is closed, the cylinder contents are

at $900$ kPa, $20\backslash$deg C$,$ and a positive work of $50$ kJ has been done against the external force.

a$)$ What is the final volume of the cylinder?

b$)$ Does this process violate the second law of thermodynamics? Answer the question by showing

all necessary calculations very clearly. If your answer is yes, comment on what may change to

make the process possible.