Question

A person's body is covered with 1.69 m^2 of wool clothing. The thickness of the wool is 1.87 × 10^-3 m. The temperature at the outside surface of the wool is 13.9 °C, and the skin temperature is 35.4 °C. How much heat per second does the person lose due to conduction?

Answer 1

The concept required to solve this problem is related to heat conductivity as a function of time.

Mathematically in a stable state the heat flux is constant and its rate of change as a function of time can be described under the function

$\frac{Q}{t} = \frac{kA\Delta T}{d}$

Where

k= Coefficient of thermal conductivity

A = Area of the object

$\Delta T$ =Temperature difference across object

d= thickness of object

According to the values given we have then,

$k_{wool} = 0.04W/mK$

$\Delta T = 35.4-13.9$

$d = 1.87*10^{-3}m$

$A = 1.69m^2$

Replacing we have,

$\frac{Q}{t} = \frac{(0.04)(1.69)(35.4-13.9)}{1.87*10^{-3}}$

$\frac{Q}{t} = 777.21J/s$

Therefore the quantity of heat per second does the person lose due to conduction is 777.21J/s