JEE MAIN - Chemistry (2025 - 23rd January Morning Shift - No. 14)
Ice at $-5^{\circ} \mathrm{C}$ is heated to become vapor with temperature of $110^{\circ} \mathrm{C}$ at atmospheric pressure. The entropy change associated with this process can be obtained from
$\int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{m}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\mathrm{m}} \text {, fusion }}{\mathrm{T}_{\mathrm{f}}}+\frac{\Delta \mathrm{H}_{\mathrm{m}, \text { vaporisation }}}{\mathrm{T}_{\mathrm{b}}}+\int_{273 \mathrm{~K}}^{373 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{m}} \mathrm{dT}+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}, \mathrm{m}} \mathrm{dT}$
$\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\text {melting }}}{273}+\frac{\Delta \mathrm{H}_{\text {boiling }}}{373}$
$\int_{268 \mathrm{~K}}^{383 \mathrm{~K}} \mathrm{C}_{\mathrm{p}} \mathrm{dT}+\frac{\mathrm{q}_{\text {rev }}}{\mathrm{T}}$
$\int_{268 \mathrm{~K}}^{273 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{m}}}{\mathrm{T}} \mathrm{dT}+\frac{\Delta \mathrm{H}_{\mathrm{m}}, \text { fusion }}{\mathrm{T}_{\mathrm{f}}}+\frac{\Delta \mathrm{H}_{\mathrm{m}, \text { vaporisation }}^{373 \mathrm{~K}}}{\mathrm{~T}_{\mathrm{b}}}+\int_{273 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{m}} \mathrm{dT}}{T}+\int_{373 \mathrm{~K}}^{383 \mathrm{~K}} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{m}} \mathrm{dT}}{\mathrm{T}}$
Explanation
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$$\begin{aligned} & \Delta \mathrm{S}_{\text {overall }}=\Delta \mathrm{S}_1+\Delta \mathrm{S}_2+\Delta \mathrm{S}_3+\Delta \mathrm{S}_4+\Delta \mathrm{S}_5 \\ & \Delta \mathrm{~S}_2=\frac{\Delta \mathrm{H}_{\mathrm{m} \text { fusion }}}{273} \mathrm{~T}_{\mathrm{f}}=273^{\prime} \mathrm{K}^{\prime} \\ & \Delta \mathrm{S}_3=\int_\limits{273}^{373} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}} \\ & \Delta \mathrm{~S}_4=\frac{\Delta \mathrm{H}_{\mathrm{m} \text { vaporisation }}}{373} \mathrm{~T}_{\mathrm{b}}=373^{\prime} \mathrm{K}^{\prime} \\ & \Delta \mathrm{S}_5=\int_\limits{373}^{383} \frac{\mathrm{C}_{\mathrm{p}, \mathrm{~m}} \mathrm{dT}}{\mathrm{~T}} \\ & \text { Answer }=(2) \end{aligned}$$
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