Conductivity physics homework

In summary: This is easy to solve. The fraction of the cross sectional area that is covered by wood is L/8. The fraction of the cross sectional area that is covered by fiberglass is L/4. Therefore, the effective thermal conductivity of a wall is L/8+L/4=L.
  • #1
beanryu
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In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is 20 degrees and the temperature outside is 0 degress . The walls and uppermost ceiling of a typical house are supported by 2*6-inch wooden beams with fiberglass insulation in between. The true depth of the beams is actually 5+5/8 inches, but we will take the thickness of the walls and ceiling to be L=18cm to allow for the interior and exterior covering. Assume that the house is a cube of length L=9.0m on a side. Assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. Ignore heat loss through the ground.

The first step is to calculate , the effective thermal conductivity of the wall (or ceiling), allowing for the fact that the 2*6 beams are actually only 1+5/8 wide and are spaced 16 inches center to center.

please help me understand the question and find the effective.
 
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  • #2
I think it's clear that once you know the thermal conductivity of the wall, the rest of the problem is easy. The key to finding the effective thermal conductivity is to decide what fraction of the wall is wood and what fraction is fiberglass. Can you do this with the information given? How is the effective conductivity then obtained?
 
  • #3
hi, i don't even know the construction of the house. the conductivity of the wood is 0.12W/m/K and the conductivity of the fiberglass insulation is 0.04 W/m/K
 
  • #4
could u help me to solve this problem now?
 
  • #5
Yes, you do know the construction of the house. You're told in detail how the walls and ceiling are constructed. In particular, you're told how wide the wood beams are and how far apart they are spaced. You are also told that fiberglass fills the space in between the beams. So what fraction of the total cross sectional area of a wall is covered by wood and what fraction is covered by fiberglass?
 

What is conductivity?

Conductivity is a measure of a material's ability to conduct electricity or heat. It is determined by the nature and structure of the material's atoms and their ability to allow the flow of charged particles.

How is conductivity measured?

Conductivity is measured using a device called a conductivity meter. This meter measures the electrical resistance of a material and converts it into a conductivity value. The unit of measurement for conductivity is Siemens per meter (S/m).

What factors affect conductivity?

Several factors can affect the conductivity of a material, including temperature, the concentration of impurities, and the type of material. In general, materials with more free electrons, such as metals, have higher conductivity than materials with fewer free electrons, such as insulators.

What is the difference between electrical and thermal conductivity?

Electrical conductivity refers to a material's ability to conduct electricity, while thermal conductivity refers to its ability to conduct heat. While both properties are related to the flow of energy, they are not always directly proportional. For example, some materials may have high electrical conductivity but low thermal conductivity, and vice versa.

How is conductivity used in real-world applications?

Conductivity plays a crucial role in many industries and technologies, including electronics, energy production and distribution, and materials science. It is also used in environmental monitoring, such as measuring the salinity of water, and in medical devices, such as EKG machines.

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