Question

A resting person takes in about 0.5 L of air in a single breath. In an hour of breathing, approximately 5 m3 of air will be breathed. Round your answer to one significant figure.

a) if air is taken in at 15C and raised in temperature to 35.8C before being exhaled, how much heat leaves the body in a day due to breathing alone? Ignore the humidification of the air in the lungs, treat air as an ideal diatomic gas and assume the pressure is 101kPa. Cp=(7/2)R. _____MJ

b) Is this heat loss significant relative to the total heat loss from the body in one day, about 9MJ? ____%

c) What is the average power (rate of heat loss) due to breathing alone? _______W

Answer 1

In an hour 5m³ air at 15C is breathed

No of moles in 5 m³ at 15 C

n = PV/RT

n = (101000 x 5)/(8.314 x 288)

n = 210.9 moles

Considering the process to be isobaric, the heat absorbed by air from the body as it goes from 15C to 35.8C

Q = nC_vΔT

Q = 210.9 x 7/2 x (35.8 - 15)

Q = 15.353 kJ/hour

Heat loss in 24 hour = 24 x 15.353 = 368.48 kJ = 0.368 MJ ANS (a)

As % of total heat loss = 0.368/9 x 100 = 4.09% ANS (b)

Rate of heat loss (power) due to breathing = 15353/3600 = 4.26 Watt ANS (c)