Two blocks of the same metal having same mass

Question:

Two blocks of the same metal having same mass and at temperature $T_{1}$ and $T_{2}$, respectively. are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, $\Delta \mathrm{S}$, for this process is :

  1. $2 \mathrm{C}_{\mathrm{P}} \ln \left(\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{4 \mathrm{~T}_{1} \mathrm{~T}_{2}}\right)$

  2. $2 \mathrm{C}_{\mathrm{P}} \ln \left[\frac{\left(\mathrm{T}_{1}+\mathrm{T}_{2}\right)^{\frac{1}{2}}}{\mathrm{~T}_{1} \mathrm{~T}_{2}}\right]$

  3. $\mathrm{C}_{\mathrm{P}} \ln \left[\frac{\left(\mathrm{T}_{1}+\mathrm{T}_{2}\right)^{2}}{4 \mathrm{~T}_{1} \mathrm{~T}_{2}}\right]$

  4. $2 \mathrm{C}_{\mathrm{P}} \ln \left[\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{2 \mathrm{~T}_{1} \mathrm{~T}_{2}}\right]$

Correct Option: , 3

Solution:

$\mathrm{C}_{\mathrm{P}} \ln \left[\frac{\left(\mathrm{T}_{1}+\mathrm{T}_{2}\right)^{2}}{4 \mathrm{~T}_{1} \mathrm{~T}_{2}}\right]$

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