$(30\%)$ A $0\mathrm{.}25m^3$ volume tank containing R$134$a is lowered into a hot geothermal pool of water in northem Califormia near the Geysers geothermal power plant. Initially the tank contains $8\%$ liquid and $92\%$ vapor by volume of the R$134$a at a temperature of $20C.$ The $90C$ water heats the R$134$a$.$ At the exit of the tank is a relief$-$valve that will allow R$134$a to exit the tank when the tank pressure exceeds $10$ bar. The process ends as the last bit of liquid in the tank evaporates. The water of the geothermal pool maintains a temperature of $90C$ and can be considered equivalent to a reversible heat transfer reservoir.

a$)$ What is the initial pressure of the tank $($ kPa $)?$

b$)$ What was the initial mass of R$134$a in the tank?

c$)$ What is the final mass of R$134$a in the tank?

d$)$ What is the heat transfer to the tank $($ kJ $)?$

e$)$ What is the entropy generation for a system that includes the tank and water heat source $(k\frac{J}{K})?$