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Second law of thermodynamics, entropy

Problem 2.152

A piece of copper of mass \(m_{1}=300 \mathrm{~g}\) with initial temperature \(t_{1}=97^{\circ} \mathrm{C}\) is placed into a calorimeter in which the water of \(\mathrm{m}\) ass \(m_{2}=100 \mathrm{~g}\) is at a temperature \(t_{2}=7^{\circ} \mathrm{C} .\) Find the entropy increment of the system by the moment the temperatures equalize. The heat capacity of the calorimeter itself is negligibly small.

Reveal Answer
 2.152. ΔS=m1c1ln⁡(T/T1)+m2c2ln⁡(T/T2)=4.4 J/K, where T=(m1c1T1+m2c2T2)/(m1c1+m2c2),c1 and c2 are the specific  heat capacities of copper and water. \begin{aligned} &\text { 2.152. } \Delta S=m_{1} c_{1} \ln \left(T / T_{1}\right)+m_{2} c_{2} \ln \left(T / T_{2}\right)=4.4 \mathrm{~J} / \mathrm{K}, \text { where }\\ &T=\left(m_{1} c_{1} T_{1}+m_{2} c_{2} T_{2}\right) /\left(m_{1} c_{1}+m_{2} c_{2}\right), \quad c_{1} \text { and } c_{2} \text { are the specific }\\ &\text { heat capacities of copper and water. } \end{aligned}
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