$(34\%),$ Air is contained in a frictionless vertical piston$-$cylinder assembly fitted with an electrical resistor. The atmosphere exerts a pressure of $100$ kPa on top of the piston, which has a mass of $40$ kg and an area of $0\mathrm{.}1m^2.$ Electrical current passes through the resistor, and the volume of the air slowly increases. During this process $2$ kJ of heat is lost to the surroundings which are at a temperature of $25C.$ The mass of the air is $0\mathrm{.}25$ kg $,$ and its temperature increases by $35C$ from an initial temperature of $50C.$ Assume the air to have constant specific heats evaluated at $25C.$ For the process determine:

a$)$ the work done by the air on the surroundings.

b$)$ the energy transfer from the resister to the air $($kJ$).$

c$)$ the change in total entropy of the air and the entropy generation

d$)$ Sketch the process on a P$-$V diagram $($label states and put numbers on both axes$).$

e$)$ Sketch the process on a T$-$S diagram $($label states and put numbers on the T axis$).$

f$)$ Determine the change in potential energy of the piston $($kJ$).$