Explaining the Insulating Effect of an Air Cavity in Terms of Heat Conduction

[pivoxa15]

Homework Statement

The textbook claims 'An air caivty between a brick outer wall and the inside wall helps to insulate from heat and cold.' It asks to explain in terms of heat conduction.

Homework Equations

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The Attempt at a Solution

Is it because it takes a certain amount of energy to get the conduction in the brick going as a brick is a poor conductor. Once it starts rolling or conducting than it becomes hard to stop it. So by installing a cavity, this momentum of conduction in the brick is stopped and for conduction to occur again, the air molecules must break a certain energy level which is hard to attain in this small cavity.

 

[Gokul43201]

No, conduction doesn't work that way. If you write down the equations relevant to conduction through a medium, you'll see why the air is important.

 

[pivoxa15]

Is it because air has a lower thermal conductivity constant than bricks. The lower the conductivity, the better the insulation.

But living in the open field with air all around you wouldn't protect you from cold or heat. So bricks are still needed. What is happening - it seems like an apparent contradiction.

 

[Gokul43201]

Is it because air has a lower thermal conductivity constant than bricks. The lower the conductivity, the better the insulation.

But living in the open field with air all around you wouldn't protect you from cold or heat.

Not if the air is already cold, and not if the air can move. Remember that there are three modes of heat transfer. Which one do you think is most responsible for transfering heat through air (over an open field)? Does this same mode play as important a role in a layer of air separating two brick walls?

 

[pivoxa15]

Not if the air is already cold, and not if the air can move. Remember that there are three modes of heat transfer. Which one do you think is most responsible for transfering heat through air (over an open field)? Does this same mode play as important a role in a layer of air separating two brick walls?

Good point. Convection is responsible for the transfer of heat through an open field. This form of heat transportation is usually much more effective than conduction, no matter how low the resistance of the solid. Correct? And that is why it can get cold and hot very quickly in the open.

The heat transfer between bricks is conduction only. My book lists the Resistance value for air as 1.0 and brick as 0.43. This implies that brick is a better conductor hence better at conducting heat than air. Hence air is a better insulator and should prevent the winter being colder and summer warmer. Although a material like polystyrene would be an even better insulator.

 

[Hootenanny]

Good point. Convection is responsible for the transfer of heat through an open field.

This form of heat transportation is usually much more effective than conduction, no matter how low the resistance of the solid.

Are you sure about that? Which warms you up quicker; standing next to a radiator or touching a radiator?

The heat transfer between bricks is conduction only. My book lists the Resistance value for air as 1.0 and brick as 0.43. This implies that brick is a better conductor hence better at conducting heat than air.

This may be true, but do not forget there are different equations which model convection as opposed to conduction.

 

[pivoxa15]

I should have mentioned that radiation from the sun is also responsible for heat transformation in the open field. In the day, this form is most dominant and the fastest of heat transformations.

Are you sure about that? Which warms you up quicker; standing next to a radiator or touching a radiator?

This may be true, but do not forget there are different equations which model convection as opposed to conduction.

Radiation is a different form of heat tranformation. I was comparing between convection and conduction.

 

[Hootenanny]

Radiation is a different form of heat tranformation. I was comparing between convection and conduction.

I meant a radiator as part of a heating system, i.e. a metal pipe through which hot water is pumped to heat a room. Let's take another example, which is hotter; standing next to an electric heater or touching the heating element with your hand?

 

[pivoxa15]

I meant a radiator as part of a heating system, i.e. a metal pipe through which hot water is pumped to heat a room. Let's take another example, which is hotter; standing next to an electric heater or touching the heating element with your hand?

Okay. Another example is which is hotter, touching a heated pot or the water in the pot? I feel these examples are unfair because the heating system is first heating the material heated by conduction and this material than heats air or liquid by convection so obvioiusly it will be hotter touching directly the first heated material.

A fair example might be a heating source such as radiation from the sun heats air in the open field and warms me by convection through air currents (It would be difficult to do this experiment because it would be hard to shield the radiation heat from the sun in the open field). Now compare that to the sun heating a brick home hence conduction and then me touching the brick. In fact I guess that the brick will feel hotter than the warmth of the air on by body.

 

[Gokul43201]

pivoxa, you can not, in general, compare heat transfer by convection in fluids with heat transfer by conduction in solids. What you can compare, are only very specific cases.

For instance, if you put your hand a foot above a cup of boiling water, do you expect it to be hotter than if you were grabbing a foot long copper rod with the bottom end dipped in the water? Might the situation be different if instead of a copper rod, it was a wooden rod?

As for the original question, a thin air layer between brick walls does not support a whole lot of convection. You can assume that heat transport through air is primarily from the conductivity of air.

 

[pivoxa15]

pivoxa, you can not, in general, compare heat transfer by convection in fluids with heat transfer by conduction in solids. What you can compare, are only very specific cases.

For instance, if you put your hand a foot above a cup of boiling water, do you expect it to be hotter than if you were grabbing a foot long copper rod with the bottom end dipped in the water? Might the situation be different if instead of a copper rod, it was a wooden rod?

I'd say in this case the convection form of heating does transfer more heat. Wouldn't you say? If a wooden one was used than even less heat would be transferred to my hand by conduction.

 

[Gokul43201]

Actually, you transfer more power through the copper rod than through air...but if that example wasn't convincing, then that's all the more reason to not go by general intuition in place of the real calculation.