Main Answer
The rate of heat conduction through the 3.00-cm-thick fur of a large animal with a 1.40-m² surface area is 60 W, assuming the animal's skin temperature is 32.0°C, the air temperature is −5.00°C, and fur has the same thermal conductivity as air.The option D is correct.
Step-by-step explanation
To calculate the rate of heat conduction through the fur, we can use Fourier's law of heat conduction, which states that the rate of heat flow through a material is proportional to the temperature gradient and the thermal conductivity of the material.
In this case, since fur has the same thermal conductivity as air, we can use the thermal conductivity of air (0.024 W/m·K) in our calculation.The rate of heat conduction through a slab of thickness x and surface area A can be calculated using the formula:Q = -kA(dT/dx).
Here, Q is the rate of heat flow (in watts), k is the thermal conductivity (in W/m·K), A is the surface area (in m²), and dT/dx is the temperature gradient (in K/m).Substituting our given values into this formula, we get:
Q = -(0.024 W/m·K)(1.40 m²)([32.0°C - (-5.00°C)]/[0.03 m]) = 60 W.
This calculation shows that under these conditions, the fur of a large animal with a surface area of 1.40 m² and a thickness of 3.00 cm can conduct away a total of 60 watts of heat from the animal's body to the cold environment outside.The option D is correct.