A student wants to loose weight. He knows that rigorous aerobic activity uses ab

Question

A student wants to loose weight. He knows that rigorous aerobic activity uses about 700 kcal/h (2900 kJ/h) and that it takes about 2000 kcal (8400 kJ) per day just to support necessary biological functions, including keeping the body warm. He decides to burn calories faster simply by sitting naked in a 22 degree C room and letting his body radiate calories away. His body has a surface area of about 1.62m^2 and his skin temperature is 34.1 degrees C. Assuming an emissivity of 1.0, at what rate(in kcal/h) will this student burn calories?

Explanation / Answer

The surface area of the body A = 1.62 m^2 The room temperature Ti = 22 + 273 = 295 K The skin temperature Tf = 34.1 + 273 = 307.1 K The emissitivity of the skin = 1.0 The Boltzman constant = 5.67*10^-8 W/m^2 K^4 The net rate at which the heat rated is                     P = A (Tf^4 - Ti^4)                        = (1)(5.67*10^-8) (1.62)[(307.1)^4 - (295)^4]                        = 121.35 W In terms of k cal                      P = 121.35(3600/4186) kcal/h                         = 104. kcal /h

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