Assuming that the human body has a 1.2-cm-thick layer of skin tissue and a surface area of 1.5m2 , estimate the rate at which heat is conducted from inside the body to the surface if the skin temperature is 34 ∘C. (Assume a normal body temperature of 37 ∘C for the temperature of the interior.)
75 J/s
To estimate the rate at which heat is conducted from inside the body to the surface, we can use the formula for heat conduction:
Q = k * A * (ΔT / d)
where Q is the heat conducted, k is the thermal conductivity of the material, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.
In this case, the material is the skin tissue, which has a temperature difference of (34 - 37) °C = -3 °C (assuming the interior temperature is 37 °C), a thickness of 1.2 cm = 0.012 m, and a surface area of 1.5 m².
The thermal conductivity of skin tissue is not readily available, but we can approximate it by using the thermal conductivity of water, which is a similar composition. The thermal conductivity of water is approximately 0.6 W/(m·K).
Now, we can calculate the rate at which heat is conducted using the formula:
Q = k * A * (ΔT / d)
Q = (0.6 W/(m·K)) * (1.5 m²) * (-3 °C) / (0.012 m)
Q ≈ -75 W
Therefore, the rate at which heat is conducted from inside the body to the surface is approximately -75 W. The negative sign indicates that heat is being transferred from the surface to the interior.