Problem $2(20$ points$)$

A piston$-$cylinder assembly is initially filled with

superheated water vapor at $900C.$ The system is

cooled down until its temperature is $150C.$ The

piston is initially in equilibrium with a constant

pressure outside of $10$ MPa $.$ The cylinder has stops

that prevent the volume to decrease below $50\%$ of

the initial volume. The temperature of the piston$-$

cylinder surface is $500$ K $.$ Calculate:

a$.$ the amount of work in $k\frac{J}{k}g.$

b$.$ the amount of heat extracted in $k\frac{J}{k}g.$

c$.$ the entropy production in $k\frac{J}{k}gK.$

d$.$ Show the process on a properly labeled sketch

of the $P-v$ diagram.