A heat pump operates on the ideal vapor$-$compression refrigeration cycle with refrigerant$-134$a as the working fluid. The refrigerant evaporates at $20$C and condenses at $1200$ kPa. The refrigerant absorbs heat from ambient air at $4$C and transfers it to a space at $24$C$.$ Determine $($a$)$ the work input and the COP, $($b$)$ the exergy destruction in each component of the cycle and the total exergy destruction in the cycle, $($c$)$ the minimum work input and the second$-$law efficiency of the cycle. $($d$)$ Determine the COP, the minimum power input, the total exergy destruction, and the exergy efficiency of the cycle if a ground$-$source heat pump is used with a ground temperature of $18$C$.$ The evaporating temperature in this case is $6$C$.$ Take everything else the same.