Question

A skier wears a jacket filled with goose down that is 16 mm thick. Another skier wears a wool sweater that is 7.0 mm thick. Both have the same surface area. Assuming the temperature difference between the inner and outer surfaces of each garment is the same, calculate the ratio (wool/goose down) of the heat lost due to conduction during the same time interval.

Answer 1

The rate of heat flow through a conductor is:H = (k A / L)  ?T  

for wool H_w = (k_w A /L_w   )  ?T            and           for goose down H_d = (k_d A / L_d )   ?T  

And take the ratio of these equations:

(H_w / H_d ) =    (k_w / L_w) / (k_d / L_d)   =  k_w L_d / k_dL_w = 0.040 *0.016 m/0.025 (0.007 m) = 3.65

Answer 2

heat lost is directly proportional to the conduction coefficient and inversely proportional to thickness.

heat los ratio = (kw / 7)/(kg/16) = (kw/kg) * ( 16/7)

where kw = conduction coeff of wool and kg is conduction coeff of goose down.

Answer 3