Waverall, 80 % of the energy used by the body must be...

Waverall, $80 \%$ of the energy used by the body must be eliminated as excess thermal energy and needs to be dissipated. The mechanisms of elimination are radiation. evaporation of sweat (2 $430 \mathrm{~kJ} / \mathrm{kg})$, evaporation from the lungs $(38 \mathrm{~kJ} / \mathrm{h})$, conduction, and convection. A person working out in a gym has a metabolic rate of $2500 \mathrm{~kJ} / \mathrm{h} .$ His body temperature is $37^{\circ} \mathrm{C}$, and the outside temperature $24^{\circ} \mathrm{C}$. Assume the skin has an area of $2.0 \mathrm{~m}^{2}$ and emissivity of $0.97$. (a) At what rate is his excess thermal energy dissipated by radiation? (b) If he eliminates $0.40 \mathrm{~kg}$ of perspiration during that hour, at what rate is thermal energy dissipated by evaporation of sweat? (c) At what rate is energy eliminated by evaporation from the lungs? (d) At what rate must the remaining excess energy be eliminated through conduction and convection?

Waverall, $80 \%$ of the energy used by the body must be eliminated as excess thermal energy and needs to be dissipated. The mechanisms of elimination are radiation. evaporation of sweat (2 $430 \mathrm{~kJ} / \mathrm{kg})$, evaporation from the lungs $(38 \mathrm{~kJ} / \mathrm{h})$, conduction, and convection.

A person working out in a gym has a metabolic rate of $2500 \mathrm{~kJ} / \mathrm{h} .$ His body temperature is $37^{\circ} \mathrm{C}$, and the outside temperature $24^{\circ} \mathrm{C}$. Assume the skin has an area of $2.0 \mathrm{~m}^{2}$ and emissivity of $0.97$. (a) At what rate is his excess thermal energy dissipated by radiation? (b) If he eliminates $0.40 \mathrm{~kg}$ of perspiration during that hour, at what rate is thermal energy dissipated by evaporation of sweat? (c) At what rate is energy eliminated by evaporation from the lungs? (d) At what rate must the remaining excess energy be eliminated through conduction and convection?

Key Concepts

Metabolic Rate

Metabolic rate refers to the amount of energy produced by the body per unit time as a result of chemical processes, especially during physical activity. It is the primary source of heat production in the body and sets the baseline for how much excess thermal energy needs to be dissipated to maintain a stable internal temperature.

Thermal Radiation

Thermal radiation is the process by which the body loses heat in the form of electromagnetic waves. This mechanism is governed by the Stefan-Boltzmann law, which relates the radiant heat energy emitted by a surface to its temperature, surface area, and emissivity. It is a key pathway for heat loss, especially in environments where the surrounding temperature is lower than the body temperature.

Evaporative Cooling

Evaporative cooling involves the removal of heat through the phase change of water from liquid to vapor. This occurs in the body via the sweating mechanism and through evaporation from the respiratory tract. The process exploits the high latent heat of vaporization of water, meaning it requires a significant amount of energy to convert liquid water into vapor, thereby removing heat from the body.

Latent Heat of Vaporization

The latent heat of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to vapor without a change in temperature. In the context of human thermoregulation, it quantifies how much energy is removed from the body when sweat or moisture in the lungs evaporates, serving as a crucial parameter in the efficiency of evaporative cooling.

Conduction and Convection

Conduction and convection are modes of heat transfer where conduction involves direct transfer of heat through a medium or between objects in contact, and convection involves the movement of warmer air or liquid away from the body, with cooler fluid replacing it. These mechanisms work in tandem to assist in dissipating the remaining heat that is not lost via radiation or evaporation.

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