A person's body is covered with 1.28 m2 of wool clothing. The thickness of the wool is 2.07 × 10-3 m. The temperature at the outside surface of the wool is 13.8 °C, and the skin temperature is 34.6 °C. How much heat per second does the person lose due to conduction?
To find the amount of heat lost due to conduction, we need to use the formula for heat transfer through conduction:
Q = (k x A x ΔT) / d
where:
Q = heat transfer (in watts)
k = thermal conductivity of the material (in watts per meter per Kelvin)
A = surface area through which heat is conducted (in square meters)
ΔT = temperature difference between the two surfaces (in Kelvin)
d = thickness of the material (in meters)
In this case, we are assuming the wool is a homogeneous material, so we can use its average thermal conductivity value. Let's assume the average thermal conductivity of wool is 0.04 W/(m·K). The temperature difference (ΔT) can be calculated as the difference between the outside surface temperature (13.8 °C) and the skin temperature (34.6 °C), converted to Kelvin.
ΔT = (34.6 - 13.8) °C + 273.15 = 60.95 K
Now we can plug in the given values into the formula:
Q = (0.04 W/(m·K)) x (1.28 m2) x (60.95 K) / (2.07 × 10-3 m)
Calculating this, we find:
Q ≈ 2.036 W
Therefore, the person loses approximately 2.036 watts of heat per second due to conduction.