An ideal refrigerator operates according to the reverse Carnot cycle and transmits heat from a cold source with water at a temperature of $27^{\circ}C$ to a boiler with water at a temperature of $100^{ \circ }C$. What amount of water must be frozen in the cooler to convert 1 kg of water into vapor in the boiler ?

Step 1:

Calculate the enthalpy of vaporization (ΔHv) at 27°C

ΔHv = 2256.6 kJ/kg

Step 2:

Calculate the amount of heat required to vaporize 1 kg of water

Q = ΔHv = 2256.6 kJ/kg

Step 3:

Calculate the amount of water that must be frozen in the cooler

Amount of water frozen = Q / (Tc - Tf)

Amount of water frozen = 2256.6 kJ/kg / (100°C - 27°C)

Amount of water frozen = 4.94 kg