Change in Entropy — Question 5

Question 5

A phase fraction changes entropy while temperature stays fixed

A .200 kg ice–water mixture is at 273 K with initial liquid mass fraction .600. Heat 10000 J is removed quasistatically at that temperature. Use $L_f=334000$ J/kg; neglect volume work and vessel capacity.

1. Find the mass that freezes and the final liquid fraction. Verify that both phases remain.

2. Find sample entropy change and the entropy gained by a reversible 273 K sink. What changes if the same heat instead reaches a 260 K reservoir?

Question 5 - Solution

A phase fraction changes entropy while temperature stays fixed

(a) Method and calculation

$$\Delta m=Q_{\mathrm{out}}/L_f=10000/334000\approx.0299401\,\mathrm{kg}.$$$$x_{\ell,f}=.600-\Delta m/.200\approx.450299,\quad0<x_{\ell,f}<1.$$

(b) Interpretation and further calculation

$$\Delta S_s=-10000/273\approx-36.6300\,\mathrm{J/K},\quad\Delta S_{273}=+36.6300\,\mathrm{J/K}.$$$$S_{\mathrm{gen,260}}=10000(1/260-1/273)\approx1.83150\,\mathrm{J/K}.$$The sample endpoint change is the same, but heat transfer to the colder sink generates entropy.

Physical check

The phase-fraction calculation must precede the assumption that the final temperature remains at coexistence.