A jogger is running outdoors on a cold day when the temperature is -20.0°C.She is breathing at the rate of 25 breaths per minute,and each time she breathes in she inhales 0.00450 m³ of air.How much thermal energy does she lose from breathing during 20.0 minutes of jogging if the air in her lungs is heated to her body temperature of 37.0°C before it is exhaled? The specific heat of air is 1020 J/kg ∙ K and the density of air under typical conditions is 1.29 kg/m³.

Question

Quizplus · Accepted Answer

The thermal energy lost can be calculated using the formula $Q = mc\Delta T$, where $m$ is the mass of air, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. First, find the total volume of air inhaled: $0.00450 \, m^3/breath \times 25 \, breaths/minute \times 20 \, minutes = 2.25 \, m^3$. The mass of this air is $2.25 \, m^3 \times 1.29 \, kg/m^3 = 2.9025 \, kg$. The temperature change is $37.0°C - (-20.0°C) = 57.0°C$. Thus, the thermal energy lost is $2.9025 \, kg \times 1020 \, J/kg∙K \times 57.0 \, K = 169,000 \, J$ or $169 \, kJ$.

A Jogger Is Running Outdoors on a Cold Day When