Q56 / 75 · JEE Main 2025 (23 Jan Shift 2) · Physics

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_z$ The change in entropy of the water, given specific heat of water is $1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, is :

  • Correct answer
    A
    $\mathrm{m} \ln \left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)$
  • B
    zero
  • C
    $\mathrm{m} \ln \left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)$
  • D
    $\mathrm{m}\left(\mathrm{T}_2-\mathrm{T}_1\right)$

Solution

$\begin{aligned} & d \mathrm{Q}=\mathrm{msdT} \\ & \mathrm{dS}=\frac{\mathrm{dQ}}{\mathrm{T}}=\frac{\mathrm{msdT}}{\mathrm{T}} \\ & \Delta \mathrm{S}=\int \frac{\mathrm{msdT}}{\mathrm{T}}=\mathrm{ms} \ln \frac{\mathrm{T}_{\mathrm{f}}}{\mathrm{T}_{\mathrm{i}}} \\ & \Delta \mathrm{S}=\mathrm{m} \ln \frac{\mathrm{T}_2}{\mathrm{~T}_1}\end{aligned}$

Hence, the correct answer is option: 'A'.

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