Question

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 260 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′Askin(Tair−Tskin), where k′ is 54 J/h⋅∘C⋅m2, the exposed skin area Askin is 1.5 m2, the air temperature Tair is 50 ∘C , and the skin temperature Tskin is 36 ∘C; (iii) the skin absorbs radiant energy from the sun at a rate of 1400W/m2; (iv) the skin absorbs radiant energy from the environment, which has temperature 50 ∘C .

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.

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 2.42×106J/kg.)

Suppose instead the person is protected by light-colored clothing (e≈0) so that the exposed skin area is only 0.450 m2 . What rate of perspiration is required now? Discuss the usefulness of the traditional clothing worn by desert peoples.

Answer 1