5. A skier wearing a fully-body ski suit of surface area 1.8 m2 is losing heat by convective and radiation processes off the surface of the ski suit at a rate of 95 W. Given that the suit is filled with goose down 15 mm thick with a thermal conductivity of 0.025 Wm−1K−1
, determine the temperature difference between the inner and outer surfaces of the ski suit.
To determine the temperature difference between the inner and outer surfaces of the ski suit, we can use the formula for thermal resistance. The thermal resistance is the ratio of the temperature difference to the heat flow rate.
The formula is as follows:
R = (thickness) / (thermal conductivity * surface area)
First, we need to convert the thickness from mm to meters, since the thermal conductivity is given in Wm^(-1)K^(-1). There are 1000 mm in 1 meter, so the thickness is 15 mm / 1000 = 0.015 m.
Now, we can substitute the values into the formula:
R = 0.015 m / (0.025 Wm^(-1)K^(-1) * 1.8 m^2)
R = 0.015 m / (0.045 WK^(-1))
R = 0.33 WK
Next, we can rearrange the formula to solve for the temperature difference:
Temperature difference = Heat flow rate / Thermal resistance
Temperature difference = 95 W / 0.33 WK
Temperature difference = 287.88 K
Therefore, the temperature difference between the inner and outer surfaces of the ski suit is approximately 287.88 K.