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Phase Transformations

Problem 2.216

A chunk of ice of mass m1=100 gm_{1}=100 \mathrm{~g} at a temperature t1=t_{1}= =0∘C=0^{\circ} \mathrm{C} was placed in a calorimeter in which water of mass m2m_{2} =100 g=100 \mathrm{~g} was at a temperature t2t_{2}. Assuming the heat capacity of the calorimeter to be negligible, find the entropy increment of the system by the moment the thermal equilibrium is reached. Consider two cases: (a) t2=60∘Ct_{2}=60^{\circ} \mathrm{C} (b) t2=94∘Ct_{2}=94^{\circ} \mathrm{C}.

Reveal Answer
\begin{aligned} &\text { (a) When } m_{2} c_{2} t_{2}<m_{1} q, \text { not all the ice will melt and }\\ &\Delta S=m_{2} c_{2}\left(\frac{T_{2}}{T_{1}}-1-\ln \frac{T_{2}}{T_{1}}\right)=9.2 \mathrm{~J} / \mathrm{K} \end{aligned} (b) When m2c2t2>m1q,m_{2} c_{2} t_{2}>m_{1} q, the ice will melt completely and ΔS=m1qT1+c2(m1ln⁡TT1−m2ln⁡T2T)=18 J/K where T=m1T1+m2Ta−m1q/c2m1+m3 \begin{array}{r} \qquad \Delta S=\frac{m_{1} q}{T_{1}}+c_{2}\left(m_{1} \ln \frac{T}{T_{1}}-m_{2} \ln \frac{T_{2}}{T}\right)=18 \mathrm{~J} / \mathrm{K} \\ \text { where } T=\frac{m_{1} T_{1}+m_{2} T_{\mathrm{a}}-m_{1} q / c_{2}}{m_{1}+m_{3}} \end{array}
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