Question

One way you keep from overheating is by perspiring.

Evaporation—a phase change—requires heat, and the heat energy

is removed from your body. Evaporation is much like boiling,

only water’s heat of vaporization at ${35}^{0}C$is a somewhat larger

$24\times {10}^{5}J/kg$Because at lower temperatures, more energy is required.

to break the molecular bonds. Very strenuous activity can

This causes an adult human to produce 30 g of perspiration per minute.

If all the perspiration evaporates, rather than drips off, at what

rate (in J/s) is it possible to exhaust heat by perspiring?

Short answer

The heat of the vaporization$\dot{q}=1200\left[\frac{\mathrm{J}}{\mathrm{s}}\right]$

Step-by-step solution

Given information

The perspiration mass flow is $30\mathrm{g}$per minute and its heat of vaporization is $24\times {10}^5\mathrm{J}/\mathrm{kg}$

formula used:

To calculate the heat exhaustion rate, we can use the following equation:

width="70">q˙=m˙ΔLv

Where width="15">m˙is the mass flow and width="18">Lvis the heat of vaporization.

calculation

Perspiration has a mass flow of:

$\begin{array}{rcl}\dot{m}& =& 30\left[\frac{g}{\min }\right]\frac{1\left[\min \right]}{60\left|s\right|}\\ & =& 0.50\left[\frac{g}{s}\right]\end{array}$

The heat of vaporization is:

$L_v=24\times {10}^5\left[\frac{\mathrm{J}}{\mathrm{kg}}\right]\frac{1|\mathrm{kg}|}{1000|\mathrm{g}|}=2400\left[\frac{\mathrm{J}}{\mathrm{g}}\right]$

Values substituted:

$\dot{q}=0.50\left[\frac{g}{s}\right]\Delta 2400\left[\frac{J}{g}\right]=1200\left[\frac{J}{s}\right]$

This number is higher than the real one because we assume that all perspiration evaporates, which is not the case.