Thermodynamics - Hard

An ideal refrigerator operates according to the reverse Carnot cycle and transmits heat from a cold source with water at a temperature of

0\,^\circ\text{C}

to a boiler with water at a temperature of

100\,^\circ\text{C}

. What amount of water must be frozen in the cooler to convert

1\,\text{kg}

of water into vapour in the boiler?