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 breathe per minute, each with volume of 0.700 L. Suppose also that you inhale dry air and exhale air at 36.0 degree 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 36.0 degree is the same as its heat of evaporation at 100 degree C .Calculate the rate at which you energy by exhaling humid air. W

Explanation / Answer

V = 0.7 L = 0.0007 m^3
P = 3.2 kPa = 3.2*10^3Pa
T = 36°C = 309K

Ideal gas law PV = NkT

N = PV/kT = (3.2x10^3)(0.0007) / (1.381×10^23)(309) = 5.249 x 10^20 water molecules
M = Nm = (5.249 x 10^20)(18.01528)(1.66 × 10^27) = 1.57 x 10^-5 kg

Latent heat of vaporization for water is 2260 kJ/kg

Q = LM = (2,260,000)(1.57 x 10^-5) = 35.48 J

18 breathes per minute = 0.3 breathes per second

Rate of energy loss = (35.48)(0.3) = 10.64 W

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