PROBLEM $1(20\%)$

A $0\mathrm{.}2-m^3$ rigid tank initially contains saturated refrigerant$-134$a vapor at $1$ MPa $.$ The tank is connected by a valve to a supply line that carries refrigerant$-134$a at $1\mathrm{.}4$ MPa and $60C.$ The valve is now opened, and the refrigerant is allowed to enter the tank. The valve is closed when one$-$half of the volume of the tank is filled with liquid and the rest with vapor at $1\mathrm{.}2$ MPa $.$ The refrigerant exchanges heat during this process with the surroundings at $25C.$ Determine $($a$)$ the amount of heat transfer and $(b)$ the exergy destruction associated with this process.