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Phase Transformations

Problem 2.217

Molten lead of mass \(m=5.0 \mathrm{~g}\) at a temperature \(t_{2}=327^{\circ} \mathrm{C}\) (the melting temperature of lead) was poured into a calorimeter packed with a large amount of ice at a temperature \(t_{1}=0^{\circ} \mathrm{C} .\) Find the entropy increment of the system lead-ice by the moment the thermal equilibrium is reached. The specific latent heat of melting of lead is equal to \(q=22.5 \mathrm{~J} / \mathrm{g}\) and its specific heat capacity is equal to \(c\) \(=0.125 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K})\)

Reveal Answer
ΔS=mq(1T1−1T2)+mc(T2T1−1−ln⁡T2T1)=0.48 J/K\Delta S=m q\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right)+m c\left(\frac{T_{2}}{T_{1}}-1-\ln \frac{T_{2}}{T_{1}}\right)=0.48 \mathrm{~J} / \mathrm{K}
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