In very cold weather a significant mechanism for heat loss...

In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is $-20^{\circ} \mathrm{C},$ what amount of heat is needed to warm to body temperature $\left(37^{\circ} \mathrm{C}\right)$ the $0.50 \mathrm{~L}$ of air exchanged with each breath? Assume that the specific heat of air is $1020 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ and that $1.0 \mathrm{~L}$ of air has mass $1.3 \times 10^{-3} \mathrm{~kg} .$ (b) How much heat is lost per hour if the respiration rate is 20 breaths per minute?

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Key Concepts

Temperature Change in Heat Transfer

Calculating the difference between the initial and final temperatures (?T) is crucial in heat transfer problems. This temperature change, when combined with the mass and specific heat capacity, determines the amount of energy required to achieve the desired temperature increase.

Rate-Based Energy Calculation

When energy transfer happens repeatedly, such as with each breath, it is necessary to calculate the cumulative energy loss over time. By determining the energy expended per event (each breath) and multiplying by the number of events per unit time (breaths per minute or hour), one can quantify total energy loss or consumption over a given period.

Specific Heat Capacity

This is a material property that indicates the amount of energy required to raise the temperature of one unit mass of a substance by one degree. In problems involving warming air or any other material, the specific heat capacity allows us to calculate how much heat energy is needed based on the mass and the change in temperature.

Mass and Density Conversion

Often, volumes are given instead of mass, so converting volume to mass becomes necessary using the density of the material. In this context, knowing the density of air allows us to calculate the mass of air in a given volume, which is then used in energy calculations.

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