A jogger is running outdoors on a cold day when the temperature is -20.0°C. Each time she breathes, she inhales 0.00450 m³ of air. She is breathing at the rate of 25 breaths per minute. How much heat does she lose from breathing during 20.0 minutes of jogging if the air in her lungs is heated to body temperature (37°C) before it is exhaled? The specific heat of air is 1020 J/(kg∙K) and the density of air 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 is equal to the mass of air inhaled times the specific heat of air times the change in temperature. The mass of air inhaled is equal to the volume of air inhaled times the density of air. The change in temperature is equal to the difference between body temperature and the temperature of the air inhaled.$$Q = mc_p \Delta T$$$$m = ho V$$$$\Delta T = T_f - T_i$$$$Q = ho V c_p (T_f - T_i)$$$$Q = (1.29 	ext{ kg/m}^3)(0.00450 	ext{ m}^3/ 	ext{breath})(25 	ext{ breaths/min})(20 	ext{ min})(1020 	ext{ J/kg K})(37°	ext{C} - (-20.0°	ext{C}))$$$$Q = 169 	ext{ kJ}$$

A Jogger Is Running Outdoors on a Cold Day When