Consider a poor lost soul walking at 5 km/h on a hot day in the desert, wearing only a bathing suit. This person’s skin temperature tends to rise due to four mechanisms:

(i) Energy is generated by metabolic reactions in the body at a rate of 280 W, and almost all of this energy is converted to heat that flows to the skin;

(ii) Heat is delivered to the skin by convection from the outside air at a rate equal to k'A_skin(Tair - T_skin), where k' is 54 J/h ∙ C° ∙ m², the exposed skin area A_skin is 1.5 m², the air temperature Tair is 47°C, and the skin temperature Tskin is 36°C;

(iii) The skin absorbs radiant energy from the sun at a rate of 1400 W/m²;

(iv) The skin absorbs radiant energy from the environment, which has temperature 47°C.

(a) Calculate the net rate (in watts) at which the person’s skin is heated by all four of these mechanisms. Assume that the emissivity of the skin is e = 1 and that the skin temperature is initially 36°C. Which mechanism is the most important?

(b) At what rate (in L/h) must perspiration evaporate from this person’s skin to maintain a constant skin temperature? (The heat of vaporization of water at 36°C is 2.42 × 10⁶ J/kg.)

(c) Suppose instead the person is protected by light-colored clothing (e ≈ 0) so that the exposed skin area is only 0.45 m². What rate of perspiration is required now? Discuss the usefulness of the traditional clothing worn by desert peoples.