Some water at 0°C is placed in a large insulated enclosure (vessel). The water vapour formed is pumped out continuously. What fraction of the water will ultimately freeze, if the latent heat vaporization is seven times the latent heat of fusion?
Correct answer: A. 7/8
- A. 7/8
- B. 8/7
- C. 3/8
- D. 5/8
Explanation
In an insulated system, the energy lost by the water that freezes must equal the energy required to vaporize the remaining water. Let m be the mass of the water and f the fraction that freezes. The heat lost by the frozen part is mfL2 and the heat gained by the vaporized part is m(1-f)L1. Given that L1 = 7L2, we have mfL2 = m(1-f)7L2. Solving for f gives f = 7/8. Therefore, 7/8 of the water freezes. The other options do not satisfy this energy balance.
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