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 breath out 22.0 breaths per minute, each with a volume of 0.600 L. Suppose also that you inhale dry air and exhale air at 37 degrees 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 37 degrees C is the same as its heat of vaporization at 100 degrees C. Calculate the rate at which you lose energy by exhaling humid air.

Explanation / Answer

Ideal gas law looks: p*v=(m/µ)*RT, where p=3.2·10^3 Pa, v=0.6 L=0.6·10^(-3) m^3, for any gas the const R=8.314, T=(273 +37)= 310°K, m is mass of exhaled vapour, µ =18 atomic mass (H2O = 1+1+16), hence m= p*v*µ / (RT) for 1 portion of exhaled water vapour; since you exhale 22 times per min, then mass exhaled per second m1=m/(24*60); to evaporate this mass you need energy per second P=m1*C, where C=2.3·10^6 Joule/kg is specific evaporation for water; thus P= p*v*µ*C / (22*60*R*T)= =3.2·10^3 *0.6·10^(-3) *18 *2.3·10^6 /(22*60*8.314*310)= = 11.1 W

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