Serway & Jewett — The First Law of Thermodynamics: Problem 38.

The rate at which a resting person converts food energy is called one’s basal metabolic rate (BMR). Assume that the resulting internal energy leaves a person’s body by radiation and convection of dry air. When you jog, most of the food energy you burn above your BMR becomes internal energy that would raise your body temperature if it were not eliminated. Assume that evaporation of perspiration is the mechanism for eliminating this energy. Suppose a person is jogging for “maximum fat burning,” converting food energy at the rate $400\text{ kcal/h}$ above his BMR, and putting out energy by work at the rate $60.0\text{ W}$. Assume that the heat of evaporation of water at body temperature is equal to its heat of vaporization at $100^{\circ}\text{C}$. (a) Determine the hourly rate at which water must evaporate from his skin. (b) When you metabolize fat, the hydrogen atoms in the fat molecule are transferred to oxygen to form water. Assume that metabolism of $1.00\text{ g}$ of fat generates $9.00\text{ kcal}$ of energy and produces $1.00\text{ g}$ of water. What fraction of the water the jogger needs is provided by fat metabolism?