ThermodynamicsHard
Question
Two blocks of copper metal are of the same size (heat capacity = C) but at different temperatures T1 and T2. These blocks are brought together and allowed to attain thermal equilibrium. The entropy change of system is
Options
A.$C\ln\left\lbrack \frac{\left( T_{2} - T_{1} \right)^{2}}{4T_{1}T_{2}} + 1 \right\rbrack$
B.$C\ln\left\lbrack \frac{\left( T_{2} - T_{1} \right)^{2}}{4T_{1}T_{2}} \right\rbrack$
C.$C\ln\left\lbrack \frac{\left( T_{2} + T_{1} \right)^{2}}{4T_{1}T_{2}} + 1 \right\rbrack$
D.$C\ln\left\lbrack \frac{\left( T_{2} + T_{1} \right)^{2}}{4T_{1}T_{2}} - 1 \right\rbrack$
Solution
Final temperature of both blocks = $\frac{T_{1} + T_{2}}{2}$
$\therefore\Delta S = \Delta S_{1} + \Delta S_{2} = C.\ln\frac{\left( T_{1} + T_{2} \right)/2}{T_{1}} + C.\ln\frac{\left( T_{1} + T_{2} \right)/2}{T_{2}} $$$= C.\ln\frac{\left( T_{1} + T_{2} \right)^{2}}{4T_{1}T_{2}}$$
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