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 heat 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. A)169 kJ B)278 kJ C)354 kJ D)431 kJ E)543 kJ

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Quizplus · Accepted Answer

The heat lost due to breathing can be calculated using the formula $Q = mc\Delta T$, where $m$ is the mass of the air, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. First, calculate the total volume of air inhaled during 20 minutes: $25 \text{ breaths/min} \times 0.00450 \text{ m}^3/\text{breath} \times 20 \text{ min} = 2.25 \text{ m}^3$. The mass of this air is $2.25 \text{ m}^3 \times 1.29 \text{ kg/m}^3 = 2.9025 \text{ kg}$. The temperature change is $37.0°C - (-20.0°C) = 57.0°C$. Thus, the heat lost is $2.9025 \text{ kg} \times 1020 \text{ J/kg} \cdot °C \times 57.0°C = 169,000 \text{ J} = 169 \text{ kJ}$.

A Jogger Is Running Outdoors on a Cold Day When