A child running a temperature of `101^(@)F` is given an antipyrine (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 min`, 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 water at that temperature is about `580 cal//g`.

Explanation

Fall of temperature = `Delta T = 101 - 98 = 3^@F`
` = 3 xx 5/9 = 5/3 ""&@C`
Mass of the child = 30 kg
Heat lost by child ` = Delta Q = mc Delta L`
` = 30 xx 1000 xx 1 xx 5/3 = 50,000` cal
Latent heat of evaporation of water `= 580 cal g^(-1)`
Water evaporated in 20 minutes = `(50000)/(580)`
Water evaporated in a minute = `(50000)/(580 xx 20) = 250/58`
` = 4.31 g "min"^(-1)`