$10\mathrm{.}32$ A geothermal heat pump operating at steady state with Refrigerant$-22$ as the working fluid is shown schematically in Fig. P$10\mathrm{.}32.$ The heat pump uses $13C$ water from wells as the thermal source. Operating data are shown on the figure for a day in which the outoide air temperature is $-6\mathrm{.}7C.$ Assume adiabatic operation of the compressor. For the heat pump, determine

$($a$)$ the volumetric flow rate of heated air to the house, in $\frac{m}{m}in.$

$($b$)$ the isentropic compressor efficiency.

$($c$)$ the compressor power, in KW $.$

$($d$)$ the coefficient of performance.

$($e$)$ the volumetric flow rate of water from the geothermal wells in L$/$min$.$

For $T_8=-6\mathrm{.}7C.$ perform a full exgery accounting of the comprescor power input, and devise and evaluate at second law efficiency for the heat pump system.