Thermodynamics

JEE Main level, single correct, medium

185 of 190

Question 185 of 190

Water of mass mm gram is slowly heated to increase the temperature from T1T_1 to TzT_z The change in entropy of the water, given specific heat of water is 1Jkg−1 K−11 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}, is :

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Answer: (A) mln⁡(T2 T1)\mathrm{m} \ln \left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)

dQ=msdTdS=dQT=msdTTΔS=∫msdTT=msln⁡TfTiΔS=mln⁡T2 T1\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}

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