Q.The heating of ice is recorded as a plot of temperature (in °C, vertical axis) against time (in minutes, horizontal axis); the sketch is not to scale. Starting from point A, the temperature stays constant along a horizontal segment AB at the melting temperature ($0\,^\circ$C) until a time $t_m$ at B. From B the temperature rises steeply along BC until it reaches $100\,^\circ$C at C. The temperature then stays constant along a horizontal segment CD at $100\,^\circ$C, and finally rises again along DE above $100\,^\circ$C. Which of the following is correct? (Note: more than one of the given options may be correct.)

Latent Heat and Change of State

When a substance changes state — solid to liquid (melting) or liquid to gas (boiling) — it absorbs heat without any change in temperature. The heat that is exchanged during this constant-temperature phase change is called latent heat. For a mass $m$ that completely changes state,

where $L$ is the specific latent heat of the substance for that transition: the latent heat of fusion $L_f$ for melting/freezing and the latent heat of vaporisation $L_v$ for boiling/condensation. The absorbed energy goes into breaking the bonds between molecules (increasing potential energy) rather than increasing their kinetic energy, which is why the temperature holds steady during the change.

Reading a heating curve. If heat is supplied at a steady rate to ice and the temperature is plotted against time, the graph has sloped segments and flat plateaus:

• A sloped segment (e.g. ice warming, or water warming from $0\,^\circ$C to $100\,^\circ$C) is governed by specific heat, $Q = mc\,\Delta T$.
• A horizontal plateau at $0\,^\circ$C is melting: ice and water coexist in equilibrium while latent heat of fusion is absorbed.
• A horizontal plateau at $100\,^\circ$C is boiling: water and steam coexist while latent heat of vaporisation is absorbed. …