Problem $2$:

A heat pump using R$-410$A heats a house to maintain it at $23C$ by using underground water at $8C$ as the heat source. The house is losing heat at a rate of $60,000k\frac{J}{h}.$ The refrigerant enters the adiabatic compressor at $280$ kPa and $-10C,$ and it leaves at $1$ MPa and $90C.$ The refrigerant exits the condenser at $0C.$ Using EES, determine

$($a$)$ the power input to the heat pump,

$($b$)$ isentropic efficiency of the compressor,

$($c$)$ the rate of heat absorption from the water,

$($d$)$ the COP of the heat pump,

$($e$)$ the Carnot COP of the heat pump,

$($f$)$ the increase in electric power input if an electric resistance heater is used instead of a heat pump, and

$($g$)$ sketch the P$-$h and T$-$s diagrams of the cycle.