Final answer:
The rate of heat conduction out of the human body can be calculated using Fourier's law of heat conduction. With given values such as the core temperature, skin temperature, tissue thickness, and surface area, the heat conduction rate is found to be 84 watts.
Step-by-step explanation:
To calculate the rate of heat conduction out of the human body, we use Fourier's law of heat conduction, which states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area through which the heat is transferred. Mathematically, this is given by:
Q' = -kA(ΔT/Δx)
where:
- Q' is the rate of heat conduction per unit time (in watts, W)
- k is the thermal conductivity of the material (in watts per meter-kelvin, W/m·K)
- A is the surface area through which heat is being transferred (in square meters, m²)
- ΔT is the temperature difference across the material (in kelvins, K or °C)
- Δx is the thickness of the material (in meters, m)
For human tissues, the thermal conductivity is typically around 0.2 W/m·K. Given the core internal temperature of 37.0°C, the skin temperature of 34.0°C, the thickness of the tissues of 1.00 cm (0.01 m), and the surface area of 1.40 m², we can calculate the heat conduction rate as follows:
Q' = -0.2 W/m·K * 1.40 m² * (34.0°C - 37.0°C) / 0.01 m
Q' = 0.2 * 1.40 * (-3.0) / 0.01
Q' = -84 W
The negative sign indicates that the direction of heat flow is from the body to the surroundings. So, the rate of heat conduction out of the human body is 84 watts.