Water of mass $m$ gram is slowly heated to increase the temperature from $T_{1}$ to $T_{2}$. The cha

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Water of mass $m$ gram is slowly heated to increase the temperature from $T_{1}$ to $T_{2}$. The change in entropy of the water, given specific heat is $1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$ is\

Professor PC Thomas Classes · Answer

(d) : Heat supplied, $\Delta Q=m s \Delta T$ Entropy change, $\Delta S=\frac{\Delta Q}{T}=\frac{m s \Delta T}{T}$\ Total change in entropy as temperature increases from\ $T_{1}$ to $T_{2}$ is\ $S_{1}-S_{2}=\int_{T_{1}}^{T_{2}} m s \frac{d T}{T}=m s \ln \left(\frac{T_{2}}{T_{1}}ight)$\ as, $s=1 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, then $\Delta S=m \ln \left(\frac{T_{2}}{T_{1}}ight)$\