How Do Material Thickness and Thermal Conductivity Affect Heat Loss in Clothing?

[moonlit]

I have two problems that I can't figure out:

1) A skier wears a jacket filled with goose down that is 15.5 mm thick. Another skier wears a wool sweater that is 7.13 mm thick. Both have the same surface area. Assuming the temperature difference between the inner and outer surfaces of each garment is the same, calculate the ratio of heat lost through wool to heat lost through goose down during the same time interval.

I know wool=0.040 and goose down=0.025 but how do I go about getting the ratio?

2) The amount of heat per second conducted from the blood capillaries beneath the skin to the surface is 200 J/s. The energy is transferred a distance of 2.4 x 10^3 m through a body whose surface area is 1.9 m^2. Assuming that the thermal conductivity is that of body fat, determine the temperature difference between the capillaries and the surface of the skin.

Do I use the equation Q=(KA delta T)t/L?

Aghhhh...help please!

 

[member 553083]

1) For this problem, you can use the ratio of the thermal conductivities of wool and goose down to determine the ratio of the heat lost through each material. The ratio of the heat lost through wool to heat lost through goose down is equal to the ratio of the thermal conductivities of wool to goose down, which is 0.040/0.025 = 1.6.2) Yes, you should use the equation Q=(KA delta T)t/L. Here, K is the thermal conductivity of body fat (which you will need to look up), A is the surface area (1.9 m^2), t is the time interval (1 second), and L is the distance (2.4 x 10^3 m). Solving for the temperature difference delta T gives you delta T = Q/(KA t/L) = 200 J/ (K x 1.9 m^2 x 1 second / 2.4 x 10^3 m).

 

[M98Ranger]

Hi there,

I can understand your frustration with these heat problems. Let's break them down step by step to help you find the solutions.

1) To find the ratio of heat lost through wool to heat lost through goose down, we need to use the equation Q = kAΔT/Δx. Here, Q represents the amount of heat lost, k is the thermal conductivity, A is the surface area, ΔT is the temperature difference, and Δx is the thickness of the material. Since the temperature difference is the same for both the wool and goose down, we can cancel it out. We also know the thickness of both materials, so we can plug in the values for k and Δx. This will give us the ratio of heat lost through wool to heat lost through goose down.

2) For this problem, we can use the equation Q = kAΔT/Δx again. Here, Q represents the amount of heat lost per second, k is the thermal conductivity (which we are given as the same as body fat), A is the surface area (given as 1.9 m^2), and Δx is the distance the heat is transferred (given as 2.4 x 10^3 m). We can rearrange the equation to solve for ΔT, which will give us the temperature difference between the capillaries and the surface of the skin.

I hope this helps you understand how to approach these problems. Don't hesitate to ask for further clarification if needed. Best of luck!