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Q10.16: NCERT Physics - Part 2 THERMAL PROPERTIES OF MATTER 10.16 Solution: A child running a temperature of 101�F is given an antipyrin…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently forget to convert the temperature difference from Fahrenheit to Celsius before applying the specific heat formula, or they incorrectly use the offset formula instead of the ratio. Since specific heat is given in cal/g°C, you must calculate $\Delta T$ in Celsius using $\Delta T_C = \Delta T_F / 1.8$ (or $9/5$), not by converting individual temperatures first.

A child running a temperature of 101�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 �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 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 cal g__.

Step-by-Step Verified Solution

**Answer:** Rate of extra evaporation = 4.31 g/min **Step-by-Step Explanation:** Temperature drop in Celsius: ΔT=101−981.8=1.67∘C\Delta T = \frac{101 - 98}{1.8} = 1.67^\circ\text{C}. Heat lost by the child's body:
Q=mcΔT=30000×1×1.67=50100 calQ = mc\Delta T = 30000 \times 1 \times 1.67 = 50100 \text{ cal}
This heat is lost by evaporation of sweat. Mass of sweat evaporated:
m=QL=50100580=86.4 gm = \frac{Q}{L} = \frac{50100}{580} = 86.4 \text{ g}
Average rate of evaporation over 20 minutes:
dmdt=86.420=4.32 g/min≈4.31 g/min\frac{dm}{dt} = \frac{86.4}{20} = 4.32 \text{ g/min} \approx 4.31 \text{ g/min}
Standard answer: 4.31 g/min .

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