Question

When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist airways. Consequently, an adult human exhales about 25 mg of evaporated water with each breath. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water’s heat of vaporization at 35°C is a somewhat larger 24 * 105 J/kg because at lower temperatures more energy is required to break the molecular bonds. At 12 breaths/min, on a dry day when the inhaled air has almost no water content, what is the body’s rate of energy loss (in J/s) due to exhaled water? (For comparison, the energy loss from radiation, usually the largest loss on a cool day, is about 100 J/s.)

Short answer

The value of power is 12 w

Step-by-step solution

Definition of power

Power defines the amount of energy that is converted with respect to time.

 Finding the power of breath 

One breath takes 5 seconds which is equivalent to 12 breaths.

The rate of mass is 0.5 mg/s

Now the heat is $Q=mL=5.{10}^{-6}\times 24\times {10}^5=12J$

Now the power is 12W