__Question 11.18__:
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 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
evaporation of water at that temperature is about 580 cal g

^{–1}.

__Solution__:*T*

_{1}= 101°F

Final temperature of the body of the child,

*T*

_{2}= 98°F

Change in temperature, Δ

*T*= [ (101 - 98) X (5/9) ]

^{o}C

Time taken to reduce the temperature,

*t*= 20 min

Mass of the child,

*m*= 30 kg = 30 × 10

^{3}g

Specific heat of the human body = Specific heat of water =

*c*

= 1000 cal/kg/ °C

Latent heat of evaporation of water,

*L*= 580 cal g

^{–1}

The heat lost by the child is given as:

∆Q = m

_{}c∆T

= 30 X 1000 X (101 - 98) X (5/9)

= 50000 cal

Let

*m*

_{1}be the mass of the water evaporated from the child’s body in 20 min.

Loss of heat through water is given by:

∆Q = m

_{1}L

∴ m

_{1}= ∆Q / L

= (50000 / 580) = 86.2 g

∴ Average rate of extra evaporation caused by the drug = m

_{1}/ t

= 86.2 / 200

= 4.3g/min

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