Question

You are considering to purchase a sleeping bag whose manufacturer claims will keep you warm to -25 °C. The bag has 4.0 cm of felt insulation. Your body produces heat at a rate of 100W. Considering only conductive heat loss, will you be able to maintain normal body temperature in the bag when the outside temperature is -25 °C? Please state any assumptions you used in this problem.

comments: I understand fourier's law generally. I am trying to solve this without assuming cross sectional area. Is this possible using thermal resistance, or cancelling area's knowing the rate of transfer is equal on both sides of sleeping bag surface. (ex. " heat flow is constant through multiple slabs, "there is same heat flow through N # of slabs) . ex R1=R2

assume 1.5 m for cross sectional area

Answer 1

assumption.

The normal body temperature as 37 degree C

Outside temperature,is

= -25 C

Area A = 1.5 m^2

Thickness, dx = 4 cm

Thermsk conductivity, K = 0.043 w/m - C

Consider heat loss rate equation for conduction.

heat loss =KAdT/dx

= 0.043 x 1.5 x (37 - (-25) / 0.04

= 99.97 W

Heat loss through bag is 99.97 W but the body produces heat at the rate of 100 W

Hence the heat loss is lower than the rate of heat production thus the bag will keep the body warm.

so we will be able to maintain the normal body temperature