JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Chemical Thermodynamics

Heating ice at 268 K to vapour at 383 K passes through five stages: warming solid ice to its melting point, melting at constant temperature, warming the liquid to its boiling point, vaporising at constant temperature, and warming the vapour to the final temperature.

For a temperature change at constant pressure, $dS=\frac{C_{p,m}dT}{T}$ (not simply $C_{p}dT$, since entropy requires dividing heat by temperature at every step); a phase change at constant $T$ and $P$ contributes $\Delta S=\frac{\Delta H_m}{T}$.

The total entropy change is

$\Delta S={\int }_{268}^{273}\frac{C_{p,m}}{T}dT+\frac{\Delta H_{m,\text{fusion}}}{T_f}+{\int }_{273}^{373}\frac{C_{p,m}}{T}dT+\frac{\Delta H_{m,\text{vap}}}{T_b}+{\int }_{373}^{383}\frac{C_{p,m}}{T}dT$