BIO A Walk in the Sun. 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’Askin (Tair - Tskin), where k’ is 54 J/h ? Co ? m2, the exposed skin area A skin is 1.5 m2, the air temperature Tair is 47o C, and the skin temperature Tskin is 36o 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 47o 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 36o 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 36o C is 2.42 X 106 J/kg.) (c) Suppose instead the person is protected by light-colored clothing 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.

Solution 127CP T=309 K T = 320 K s The heat absorbed is q=mL a) i) 280 W 0 2 2 0 ii)(54 J/h.C .m )(1.5 m (11 C )/3600 s/h = 0.248 W 3 iii)(1400 w/m )(1,5 m ) = 2.1 × 10 W iv)5.67 × 10 W/m (1.5 m )[(320 K ) (309K) ] = 116 W 4 The total is 2.50 kW ,with the largest portion due to radiation from the sun 3 b) P = 2.5×10 W 6 Lv 1000 kg/m (2.42×10 J/kg.K) = 1.03 × 10 m /s. this is equal to 3.72 L/h c)the above calculations with e=o and the decreased area gives a power of 945 W and a corresponding evaporation rate of 1.4 L/h.wearing reflective clothing helps a good deal.Large areas of loose-weave clothing also facilitate evaporation.