An ice$-$making machine operates in a Carnot cycle. It takes heat from water at $0\mathrm{.}0\backslash$deg C and rejects heat to a room at $20\mathrm{.}0\backslash$deg C$.$ Suppose that $85\mathrm{.}0$ kg of water at $0\mathrm{.}0\backslash$deg C are converted to ice at $0\mathrm{.}0\backslash$deg C$.($a$)$ How much heat is discharged into the room? $($b$)$ How much energy must be supplied to the device?