Assume a goose has a 2.0-cm-thick layer of feather down (on average) and a body surface area of 0.14 m2 . What is the rate of heat loss (conduction only) if the goose, with a body temperature of 41 ∘C, is outside on a winter day when the air temperature is 6 ∘C?
To calculate the rate of heat loss through conduction, we can use the formula:
Q = k * A * ΔT / d
Where:
Q is the rate of heat loss (in watts)
k is the thermal conductivity of air (in watts per meter per degree Celsius)
A is the surface area of the goose's body (in square meters)
ΔT is the temperature difference between the goose's body and the air (in degrees Celsius)
d is the thickness of the feather down layer (in meters)
First, we need to convert the given temperatures into Kelvin since the formula uses the absolute temperature scale.
T_body = 41 °C + 273.15 = 314.15 K
T_air = 6 °C + 273.15 = 279.15 K
Next, we need to find the thermal conductivity of air. The thermal conductivity of air is approximately 0.026 W/(m·K).
Now we can substitute the given values into the formula:
Q = 0.026 * 0.14 * (314.15 - 279.15) / 0.02
Calculating this gives us the rate of heat loss through conduction.