Question $7(20$ points$)$

Cold water at $10C$ enters a water heater at the rate of $0\mathrm{.}02m\frac{3}{m}in$ and leaves the water heater at $50C.$

The water heater receives heat from a heat pump that receives heat from a heat source at $0C.$

$($a$)$ Assuming the water to be an incompressible liquid that does not change phase during heat addition,

determine the rate of heat supplied to the water, in $k\frac{J}{s}.(10$ points$)$

$($b$)$ Assuming the water heater acts as a heat sink having an average temperature of $30C,$ determine the

minimum power supplied to the heat pump, in kW $(10$ points$)$