A $27$ kg iron block initially at $375$ C is quenched in an insulated tank that contains $133$kg of water at $25$ C$.$ Assume the water that vaporizes during the process condenses back in the tank and the surroundings are at $13$ C and $123$ kPa. The specific heats of iron and water are $0\mathrm{.}45$ kJ$/$kgK and $4\mathrm{.}18$ kJ$/$kgK$,$ respectively. a: Determine the final equilibrium temperature. b: Determine the entropy change of the combined system at the initial state. c: Determine the exergy of the combined system at the initial state. d: Determine the waste work potential during this process.