Question

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 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°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/m^3.

Answer 1

Answer: 168606 J

Explanation:

Amount of heat lost is given by:

Q = m c ΔT

where, m is the mass of air inhaled, c is the specific heat of air and ΔT is the change in the temperature.

First, we will calculate the mass of air inhaled.

In each breath, jogger inhales 0.00450 m³ of air.

Breathing rate = 25 breathes per minute.

She jogs for 20 minutes.

So amount of air inhaled = 25 breathes per minute × 20 minutes × 0.00450 m³

Mass of air inhaled = density of air × volume of air inhaled

⇒ m = 1.29 kg/m³× 25 breathes per minute × 20 minutes × 0.00450 m³  

⇒ m = 2.9 kg

Now, ΔT = T₂-T₁

T₁ = -20⁰C = -20 +273 K = 253 K

T₂ = 37⁰C = 37+273 K = 310 K

⇒ ΔT = T₂-T₁ = 310 K- 253 K = 57 K

Q = m c ΔT

⇒ Q = 2.9 kg × 1020 J/kg.K × 57 K = 168606 J

Thus, the jogger losses 168606 J amount of heat from breathing during 20 minutes of jogging.