## Thermal Insulation

A mountain climber wears down clothing 3.56 cm thick with total surface area 1.80 m2. The temperature at the surface of the clothing is -19.7°C and at the skin is 33.1°C. Determine the rate of heat flow by conduction through the clothing assuming it is dry and that the thermal conductivity of down is k = 0.025 J/(s·m·C°).

**66.7000 W****Approach**

This problem is asking how fast heat is transferred from the high temperature (33.1°C) to the low temperature (-19.7°C) through the insulating clothing, i.e., heat per second.

## Solution

The rate heat is transferred is given by

Q/t=kA*(T1-T2/l)

Here k = 0.025 J/(s·m·C°), A = 1.80 m2, T1 = 33.1°C, T2 = -19.7°C and l = 3.56/100 m. Putting the values into the equation gives Q/t = 66.7 W.

Q/t=kA*(T1-T2/l)

Here k = 0.025 J/(s·m·C°), A = 1.80 m2, T1 = 33.1°C, T2 = -19.7°C and l = 3.56/100 m. Putting the values into the equation gives Q/t = 66.7 W.