The top layer of your goose down sleeping bag has a thickness of 5.0 cm and a surface area of 1.0 m^2. When the outside temperature is -18 degrees celcius you lose 24 Cal/hr by heat conduction through the bag (which remains at a cozy 34 degrees celcius inside). Assume that you're sleeping on an insulated pad that eliminates heat conduction to the ground beneath you. What is the thermal conductivity of the goose down?
Duplicate post; already answered
0.03
To find the thermal conductivity of the goose down, we can use the formula for heat conduction:
Q = k * A * (ΔT / d)
Where:
Q is the rate of heat conduction (in this case, 24 Cal/hr),
k is the thermal conductivity of the material (what we're trying to find),
A is the surface area of the material (1.0 m^2),
ΔT is the temperature difference between the inside and outside (34 - (-18) = 52 degrees Celsius),
and d is the thickness of the material (5.0 cm or 0.05 m).
Rearranging the formula to solve for k, we have:
k = Q / (A * (ΔT / d))
Substituting the given values, we have:
k = 24 Cal/hr / (1.0 m^2 * (52°C / 0.05 m))
First, we need to convert the heat transfer rate from Calories per hour to Joules per second (or Watts). 1 Cal/hr is equivalent to 4.184 J/s.
k = (24 * 4.184 J/s) / (1.0 m^2 * (52°C / 0.05 m))
Simplifying the equation:
k = 99.96 J/s / (1.0 m^2 * (52°C / 0.05 m))
k = 99.96 / (1.0 * (52 / 0.05))
k = 99.96 / (52/0.05)
k = 99.96 / (1040)
k ≈ 0.096 J/(s·m·°C)
Therefore, the thermal conductivity of the goose down is approximately 0.096 J/(s·m·°C).