The excess internal energy of metabolism is exhausted through a variety of chann

Question

The excess internal energy of metabolism is exhausted through a variety of channels, such as through radiation and evaporation of perspiration. Consider another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 18.0 breaths per minute, each with a volume of 0.590 L. Suppose also that you inhale dry air and exhale air at 42.6°C containing water vapor with a vapor pressure of 3.20 kPa. The vapor comes from the evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume its latent heat of evaporation at 42.6°C is the same as its heat of vaporization at 100°C. Calculate the rate at which you lose energy by exhaling humid air.

............W

Explanation / Answer

18 breathe per minute =0.30 breathes per second

V = 0.59 L or 0.00059 m^3
P = 3.2 kPa
T =42.6° Celcius or 315.7 Kelvin

PV = NkT

N = PV/kT = (3.2x10^3)(0.00059) / (1.381×10^23)(315.7) = 4.33 x 10^20 water molecules
M = Nm = (4.33 x 10^20)(18.01528)(1.66 × 10^27) = 1.295 x 10^-5 kg

Latent heat of vaporization for water is 2260 kJ/kg

Q = LM = (2,260,000)(1.295 x 10^-5) = 29.267 J

Rate of energy loss = (29.267)*(0.30) = 8.78 W

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