Question

A recruit can join the semi-secret “300 F” club at the Amundsen–Scott South Pole Station only when the outside temperature is below –70°C. On such a day, the recruit first basks in a hot sauna and then runs outside wearing only shoes. (This is, of course, extremely dangerous, but the rite is effectively a protest against the constant danger of the winter cold at the south pole.) Assume that upon stepping out of the sauna, the recruit's skin temperature is 104°F and the walls, ceiling, and floor of the sauna room have a temperature of 32°C. Take the recruit's surface area to be 1.7 m2, and take the skin emissivity to be 0.75. (a) What is the approximate net rate Pnet at which the recruit loses energy via thermal radiation exchanges with the room? Next, assume that when outdoors, half the recruit's surface area exchanges thermal radiation with the sky at a temperature of –24°C and the other half exchanges thermal radiation with the snow and ground at a temperature of –79°C. What is the approximate net rate at which the recruit loses energy via thermal radiation exchanges with (b) the sky and (c) the snow and ground?

Answer 1

Answer:

(a) approximate net rate = e $\sigma$ A (T⁴ - T₀⁴) = 0.75 x 5.67 x 10^-8 x 1.7 x (313⁴ - 305⁴) = 68.26 W

(b) with the sky = 0.75 x 5.67 x 10^-8 x (1.7/2) x (313⁴ - 249⁴) = 207.9 W

(c) the snow and ground =  0.75 x 5.67 x 10^-8 x (1.7/2) x (313⁴ - 194⁴) = 295.7 W