A jogger is running outdoors on a cold day when the temperature is $- 20.0 ^ { \circ } \mathrm { C }$ she is breathing at the rate of 25 breaths per minute, and each time she breathes in she inhales $0.00450 \mathrm {~m} ^ { 3 }$ 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 $37.0 ^ { \circ } \mathrm { C }$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg }$ K and the density of air under typical conditions is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question

A jogger is running outdoors on a cold day when the temperature is $- 20.0 ^ { \circ } \mathrm { C }$ she is breathing at  the rate of 25 breaths per minute, and each time she breathes in she inhales $0.00450 \mathrm {~m} ^ { 3 }$ 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 $37.0 ^ { \circ } \mathrm { C }$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg }$ K and the density of air under typical conditions is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Quizplus · Accepted Answer

The heat lost 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, find the total volume of air inhaled: $0.00450 \, \text{m}^3/\text{breath} \times 25 \, \text{breaths/min} \times 20.0 \, \text{min} = 2.25 \, \text{m}^3$. 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 $37.0 - (-20.0) = 57.0 ^\circ\text{C}$. Thus, $Q = 2.9025 \, \text{kg} \times 1020 \, \text{J/kg}^\circ\text{C} \times 57.0 ^\circ\text{C} = 169,014.45 \, \text{J} \approx 169 \, \text{kJ}$.

A Jogger Is Running Outdoors on a Cold Day When −20.0∘C- 20.0 ^ { \circ } \mathrm { C }−20.0∘C

A Jogger Is Running Outdoors on a Cold Day When $- 20.0 ^ { \circ } \mathrm { C }$