Question

The fiber artist spins a 100% wool yarn with a radius of 0.5cm that she wants to use to weave a blanket. If she wove the blanket in a way that at any point it was double the thickness of the yarn, How much heat would the blanket allow to escape? Assume it will be used in her home that she keeps at 20℃. The thermal conductivity of sheep wool is 0.039 W/mk.

Answer 1

To calculate the heat that the blanket allows to escape, we need to first calculate the thermal conductivity of the blanket. The thermal conductivity of sheep wool is given as 0.039 W/mk. Since the blanket is double the thickness of the yarn, the thickness would be 2(0.5cm) = 1cm = 0.01m.

The rate of heat transfer through conduction is given by the equation Q = (k * A * ΔT) / d, where Q is the heat transfer, k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and d is the thickness.

Here, the cross-sectional area of the yarn would be the circumference of the yarn multiplied by the thickness, which is 2πr * d. Considering that the blanket at any point is double the thickness of the yarn, the cross-sectional area would be 2(2π * 0.01m * 0.005cm).

Assuming that the blanket is a square, the surface area would be 4 times the cross-sectional area. Therefore, the surface area would be 4(2(2π * 0.01m * 0.005cm)).

The temperature difference would be the difference between the temperature of the blanket and the temperature of the environment, which is 20℃.

Finally, we can substitute these values into the heat transfer equation to calculate the heat that the blanket allows to escape.

Learn more about Heat transfer through conduction