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### Course: Physics library>Unit 10

Lesson 2: Specific heat and heat transfer

# Intuition behind formula for thermal conductivity

Intuition behind formula for thermal conductivity.

## Want to join the conversation?

• But when we increase the thickness of the wall, it doesn't affect the amount of thermal energy transferred, doesn't it? All it does is that it takes a longer time to get transferred from one side to the other? So how can we say that it helps with insulation? Im sorry if if my question is too confusing.
• Your right it only delays the transfer of heat energy. If you put an insulation box in the contact with heat ,the time will come when inside and outside temp of box will be same. But suppose there is hot sunny day and you are in the metal house it will quickly become hot, you have thick layers of Polystyrene or Styrofoam on the walls, it will slow down the heat transfer and may be before thermal equilibrium there will be sunset and night, or small cooling system will work.
• Why doesn't the heat transfer speed depend on the absolute temperatures themselves?

I mean, Imagine 600 Kelvin degree and 500 Kelvin degree temperatures, the molecules are moving really fast, and the time delay between collisions of a molecule with the wall is short.

But if you have like 105 kelvin degree and 5 kelvin degree temperatures, the molecules would move much slower, and therefore it would them more time to get to the wall, so the collisions wouldn't only be weaker than in the case with 600 and 500 degree temperatures, but they would also be happening less often.. wouldn't they?

So why don't the temperatures themselves affect the heat transfering speed?
• Orangus, what you said is correct, though not in contradiction to what Sal was saying in the video. Sal was explaining the "Intuition behind the formula for thermal conductivity," he was not solving for specific heat ratios. Think about your question then watch the video again and you will see that Sal is reenforcing your point using generalized intuition as opposed to specifics. There are reasons he teaches this way and they are all good ones. It is much more powerful to know the system than it is to know the design, because if you have a good intuition for the general principals you will, generaly, be able to figure out the specifics. Also, Sal himself actually answers your question at around the mark. (Ta - Tb)
I hope this helped, Happy Learning:)
• I still don't get it. We derived this formula on the basis of one assumption.i.e there exists a steady state. But I've rummaged through google and I still couldn't find the answer for the question as to why heat flows in the first place. Like, from what I've been reading in books, is the fact that the temperature is constant everywhere along the conductor during steady state.So , why does heat flow in the first place?
• Heat flows through contact whenever there`s a temperature gradient. In other words, if two points have different temperatures and are connected by a thermal conductor, heat will flow between them.
Heat flows espontaneously only from the hot source to the cold source.
• What do we do if one side of the wall has a greater area than the other side of the wall? For example, in sal's sphere, as long as the sphere had some thickness, the outside of the sphere would have a greater surface area than the inside of the sphere. Which side of the sphere should we put into the equation?
• When we consider total heat transfer over some time t,
Q=k*A*dT*dt/thickness
but won't the temperature differential (dT) change (reduce) with a change in time(dt)?

Shouldn't it deal with something like integrating the LHS wrt dt as dT changes(reduces)?
• sir
can you make a video on the concept of thermal diffusivity {including the formula derivation}? Please...
• Does the temperature of the barrier affect the equation?
• What Sal should have said is that one side of the barrier (think of it as the interior of a wall) had surface temperature of Ta and the other side (exterior) had a surface temperature of Tb.

The temperature of the barrier itself varies linearly from one side to the other.

Also, the thermal conductivity CAN very with temperature, but just don't worry about that.
(1 vote)
• Why if I increase the area of the surface the rate heat transference increase? It doesnt makes sense if i have to cover more area the transference will decrease.
(1 vote)
• Each particle of the surface is involved in the conduction of heat, a bigger surface area means there are more particles working on transferring heat from the hot side to the cooler side. This is why a room with bigger windows will loose more heat than a room with smaller windows even if they are made of the same type of glass and are the same thickness.

It is increasing the thickness of the material that decreases heat transfer as the heat needs to travel through more particles (further) to escape.
• What if there was no wall between the gases?, would there be no thickness of the wall and K would be the ratio constant between two gases?
(1 vote)
• If there were no wall between the gasses they would freely mix and there would be mixing of the gasses as well as some heat flow.

With ideal gases there are no collisions between the gas molecules/atoms so there would be no heat transfer between the gases but the system would come to an equilibrium as the gases mix.