An ice$-$making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at $0\mathrm{.}0$C and rejects heat to a room at a temperature of $19\mathrm{.}9$C$.$ Suppose that liquid water with a mass of $78\mathrm{.}6$ kg at $0\mathrm{.}0$C is converted to ice at the same temperature.

Take the heat of fusion for water to be Lf $=3\mathrm{.}34105$ J$/$kg$.$

a$)$ How much heat $|$QH$|$ is rejected to the room?

b$)$ How much energy E must be supplied to the device?