Evaporation of sweat is an important mechanism for...

Evaporation of sweat is an important mechanism for temperature control in some warm-blooded animals. (a) What mass of water must evaporate from the skin of a 70.0-kg man to cool his body 1.00 $\mathrm{C}^{\circ} ?$ The heat of vaporization of water at body temperature $\left(37^{\circ} \mathrm{C}\right)$ is $2.42 \times 10^{6} \mathrm{J} / \mathrm{kg} .$ The specific heat of a typical human body is 3480 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$ (see Exercise 17.31$) .$ (b) What volume of water must the man drink to replenish the evaporated water? Compare to the volume of a soft-drink can $\left(355 \mathrm{cm}^{3}\right)$.

Key Concepts

Mass-Volume Conversion (Density Concept)

Mass-volume conversion is based on the density of a substance, which links its mass and its volume. When dealing with substances like water, converting between the mass evaporated and the volume that needs to be ingested or replenished is crucial. This concept allows us to relate physical quantities measured in different units, such as kilograms and liters or cubic centimeters.

Energy Conservation in Thermal Processes

The principle of energy conservation in thermal processes involves the idea that energy must be balanced when a system gains or loses heat. In this context, the energy required to cool a body must be accounted for by the energy absorbed during evaporative processes, establishing a quantitative relationship between the thermal energy change of the body and the mass of water that evaporates.

Specific Heat Capacity

Specific heat capacity is a material property that describes the amount of heat energy required to change the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). It is a central concept in thermodynamics as it relates to how substances respond thermally to energy absorption or loss, and is used to calculate the energy change involved when a body experiences a temperature change.

Latent Heat of Vaporization

The latent heat of vaporization is the amount of energy required to transform a unit mass of a liquid into a gas at a constant temperature. This concept is essential in understanding phase changes, particularly in cooling mechanisms such as evaporation, where energy is absorbed from the surroundings during the liquid-to-gas transition, leading to a cooling effect.

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