Suppose A Large Animal Has 2.75 Cm Thick Fur With
According to the text, thermal conductivity is an intensive property that measures a substance's ability to conduct heat. In heat transfer, it is represented by the letter "k" and is measured in units such as Btu(IT)/(ft h°F) or kcal/(m h°C). The thermal conductivity of air at 0°C is much lower compared to other substances, such as copper or carbon allotropes. The viscosity of air is dependent on temperature and ranges from 1.81 × 10-5 kg/(m·s) to 1.81 × 10-5 Pa·s at 15 °C. Lastly, air has a poor thermal conductivity of 2.623−6.763 × 10−2 W m−1 K−1 between 300 and 900 K.
The rate of heat conduction through the fur of the animal can be calculated using the formula:
[ \text{Rate of heat conduction} = k \times A \times \frac{T_s - T_a}{d} ]
Where:
- ( k ) is the thermal conductivity
- ( A ) is the surface area
- ( T_s ) is the skin temperature
- ( T_a ) is the air temperature
- ( d ) is the thickness of the fur
Given that the fur has the same thermal conductivity as air, and the thermal conductivity of air is in the range of 2.623−6.763 × 10−2 W m−1 K−1, we can use the average value.
Substituting the given values:
- ( k = 4.6935 × 10−2 , \text{W m}^{-1} , \text{K}^{-1} ) (average thermal conductivity of air at the given range)
- ( A = 1.15 , \text{m}^2 )
- ( T_s = 32.0°C )
- ( T_a = -5.00°C )
- ( d = 2.75 \times 10^{-2} , \text{m} )
Now, we can calculate the rate of heat conduction:
[ \text{Rate of heat conduction} = 4.6935 × 10−2 \times 1.15 \times (32.0 - (-5.00)) / 2.75 \times 10^{-2} ]
[ \text{Rate of heat conduction} \approx 944.57 , \text{W} ]
Therefore, the rate of heat conduction through the fur of the animal is approximately 944.57 watts.
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