A person has a body surface area of 1.8 m2 and is wearing insulated clothing wit

Question

A person has a body surface area of 1.8 m2 and is wearing insulated clothing with an average thermal conductivity of 0.040 J/s.m.oC and a thickness of 0.010 m. The person's skin surface temperature is 33o C and the temperature at the outer surface of the clothing is -5o C.

(a) Calculate the rate of thermal energy loss by conduction from the person's body. (Two significant figures)
J/s

(b) Calculate the number of jelly doughnuts the person would have to consume to maintain body temperature for one hour. (One jelly doughnut supplies 1046 kJ (250 Calories; 1 Calorie = 4186 J.)) Round the answer to the nearest whole jelly doughnut.


(c) The person falls into some wet snow and the clothing becomes wet, with a thermal conductivity of 0.50 J/s.m.oC, close to that of water. Calculate the number of jelly doughnuts the person would have to consume to maintain body temperature for one hour under these conditions. Round the answer to the nearest whole jelly doughnut.

Explanation / Answer

We use H = kA*(Th - Tc)/L = 0.040W/m-K*1.8m^2*(33 - -5)/0.010m = 274W b) The energy in hour = 274J/s*3600s = 986400J So each doughnut contains 250*4186 = 1046500J...the person would have to consume 986400/1046500 = 0.94 doughnuts c) Now H = kA*(Th - Tc)/L = 0.50W/m-K*1.8m^2*(33 - -5)/0.010m = 3420W So in 1 hour E = P*t = 3420*3600 = 12312000J So the number of doughnuts = 12312000J/1046500J = 11.8 doughnuts

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