Calculating Total Rate of Conduction of Heat Through Clothing

In summary, the conversation discusses a mountain climber with a body surface of 1.80 m2 and 1.00 X 10-2 m thick fibrous clothing. The climber's skin temperature is 33.1 ºC while the outer surface of his clothing is at 273.15 K. The total rate of conduction of heat through his clothing is calculated using the thermal conductivity of his dry clothing (0.0400 W m-1 K-1) and the thermal conductivity of water (0.61 W m-1 K-1). The final calculations for (a) and (b) result in 238.32W and 3634.38W, respectively, with the reminder
  • #1
Priscilla
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Homework Statement



A mountain climber has a body surface of 1.80 m2 and wears fibrous clothing 1.00 X 10-2 m thick. He has a skin temperature of 33.1 ºC while the outer surface of his clothing is at 273.15 K. Calculate the total rate of conduction of heat through his clothing in Watts,
(a) taking the thermal conductivity of his dry clothing to be 0.0400 W m-1 K-1,
(b) assuming that that clothing is wet through and that the appropriate thermal conductivity is that of water (0.61 W m-1 K-1).

Homework Equations



P=kA (delta T/ delta x)

The Attempt at a Solution



a) P= (0.0400W/mK)(1.80m^2)[(33.1ºC - 0ºC)/ 1.00e-2 m) = 238.32W
b) P = (0.61W/mK)(1.80m^2)[(33.1ºC - 0ºC)/1.00e-2 m) = 3634.38W
 
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  • #2
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1. How do you calculate the total rate of conduction of heat through clothing?

To calculate the total rate of conduction of heat through clothing, you need to know the thermal conductivity of the fabric, the thickness of the clothing, and the temperature difference between the inner and outer layers of the clothing. Then, you can use the formula Q = kA(T2-T1)/d, where Q is the rate of heat conduction, k is the thermal conductivity, A is the surface area, T2 and T1 are the temperatures of the inner and outer layers, and d is the thickness of the clothing.

2. What is thermal conductivity and how does it affect the rate of conduction through clothing?

Thermal conductivity is a measure of how well a material can transfer heat. Materials with high thermal conductivity, such as metals, can transfer heat quickly, while materials with low thermal conductivity, such as air, transfer heat slowly. In clothing, materials with higher thermal conductivity will allow heat to pass through more easily, while materials with lower thermal conductivity will act as insulators and slow down the rate of conduction.

3. How does the thickness of clothing affect the rate of conduction of heat?

The thickness of clothing plays a role in the rate of conduction of heat by increasing the distance that heat must travel through the fabric. Thicker clothing will have a higher thermal resistance, which means heat will take longer to pass through it. This can help keep the body warm in cold environments, but can also lead to discomfort if the clothing is too thick and traps too much heat.

4. What factors can affect the accuracy of calculating the total rate of conduction of heat through clothing?

There are several factors that can affect the accuracy of calculating the total rate of conduction of heat through clothing. These include the type of fabric and its thermal properties, the construction of the clothing (such as layers or insulation), the fit of the clothing, and environmental factors such as humidity and wind. Additionally, individual factors such as body heat and activity level can also impact the rate of heat conduction through clothing.

5. Can the total rate of conduction of heat through clothing be reduced or increased?

Yes, the total rate of conduction of heat through clothing can be reduced or increased depending on various factors. Wearing thicker or more insulating clothing can slow down the rate of heat conduction and keep the body warm in cold temperatures. On the other hand, wearing lighter and more breathable clothing can increase the rate of heat conduction, making it more suitable for warmer environments. Other factors such as changing environmental conditions or adjusting the fit of the clothing can also impact the rate of heat conduction through clothing.

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