Q.A child running a temperature of $101\ ^\circ\text{F}$ is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to $98\ ^\circ\text{F}$ in $20$ minutes, what is the average rate of extra evaporation caused, by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is $30\ \text{kg}$. The specific heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about $580\ \text{cal g}^{-1}$.

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. …