(a)By how much would the body temperature of the bicyclist in Problem 17.89 increase in an hour if he were unable to get rid of the excess heat? (b) Is this temperature increase large enough to be serious? To find out, how high a fever would it be equivalent to, in °F? (Recall that the normal internal body temperature is 98.6°F and the specific heat of the body is$\mathbf{3480}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{kg}{\mathbf{.}}^{\mathbf{0}}\mathbf{}\mathbf{C}$

From the problem 17.89, the total heat energy developed in the body is,

$\mathrm{Q}=1.44\mathrm{x}{10}^6\mathrm{J}$

If this amount of heat is developed in body and there is no way to release it then this will lead to an increase in body temperature.

Mass of the bicyclist is 70 kg.

Use the specific heat equation to calculate the rise in temperature,

$$\begin{gathered} \mathrm{Q}=\mathrm{mC}∆\mathrm{T} \\ ∆\mathrm{T}=\frac{\mathrm{Q}}{\mathrm{mC}} \\ =\frac{1.44\times {10}^6\mathrm{J}}{70\mathrm{Kg}\mathrm{x}3480\mathrm{J}/{\mathrm{Kgx}}^{°}\mathrm{C}} \\ =5.9^{°}\mathrm{C} \end{gathered}$$

Thus the rise in body temperature is by 5.9ºC.

The conversion relation of Celsius to Fahrenheit is,

$9{\mathrm{F}}^{°}=5{\mathrm{C}}^{°}$

Therefore,

$$\begin{gathered} ∆\mathrm{T}=\left(5.9^{°}\mathrm{C}\right)\left(\frac{9^{°}\mathrm{F}}{5^{°}\mathrm{C}}\right) \\ =10.6^{°}\mathrm{F} \end{gathered}$$

Thus, the final body temperature of the bicyclist is,

localid="1668060018533" $$\begin{gathered} \mathrm{T}=98.5^{°}\mathrm{F}+10.6^{°}\mathrm{F} \\ =10.9^{°}\mathrm{F} \end{gathered}$$

For adults, the maximum body temperature which is safe and normal is 99ºF. Thus, the temperature localid="1668060022591" ${109}^{°}\mathrm{F}$is way more than what is normal and can cause severe health issues.