Can gas kinetic theory explain heat transfer from gas to a container?

In summary, kinetic theory can be used to determine the thermal conductivity of the gas, and the thermal conductivity can be used in a heat transfer analysis to get the thermal flux.
  • #1
cmb
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If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

I understand the basics of explaining and calculating pressure with the kinetic theory of gases, but if we assume energy is transferred between the gas molecules and those of the container in each component collision, can this give us an estimate of heat flux between the contained gas and the container, if they are at different temperatures?
 
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  • #2
cmb said:
Summary: If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

I understand the basics of explaining and calculating pressure with the kinetic theory of gases, but if we assume energy is transferred between the gas molecules and those of the container in each component collision, can this give us an estimate of heat flux between the contained gas and the container, if they are at different temperatures?
Do you think that it is possible for temperature to vary with spatial position in a gas? Or do you think that the temperature is discontinuous at the interface between the gas and the container?
 
  • #3
Of course, but I have no view on that. The question is whether the thermal flux can be approximated by kinetic theory, and if that requires an estimate of thermal gradient in the gas then, sure, how could that be calculated to get to that end point?

This is a straight question, not a piece of homework where I have much clue myself.
 
  • #4
cmb said:
Of course, but I have no view on that. The question is whether the thermal flux can be approximated by kinetic theory, and if that requires an estimate of thermal gradient in the gas then, sure, how could that be calculated to get to that end point?

This is a straight question, not a piece of homework where I have much clue myself.
Kinetic theory can be used to determine the thermal conductivity of the gas (see Transport Phenomena by Bird, Stewart, and Lightfoot), and the thermal conductivity can be used in a heat transfer analysis to get the thermal flux. Is that a satisfactory approach?
 
  • #5
I think the answer is 'no', then?

Where two objects collide in an elastic collision, where one is stationary (by definition as the inertial frame), they share the momentum of the incoming object. What I was thinking was that there might be a model of a gas as a series of 'objects' coming into collision with 'stationary objects' in the container wall. Then we might conclude an exchange of momentum from that.

The momentum the 'wall objects' have received will therefore warm up the wall as they are bound into the wall.

Eventually, some equilibrium will be reached where the 'wall objects' are oscillating fast enough that an exchange of momentum is just as likely to the gas objects as from them.

With that model in mind, I was wondering if it might reveal the thermal flux across the gas/solid boundary?
 
  • #6
Check out the development in Bird et al and see what you think.
 
  • #7
OK. Where can I read a copy?
 

1. How does gas kinetic theory explain heat transfer from gas to a container?

The gas kinetic theory explains heat transfer from gas to a container by stating that the molecules of gas have kinetic energy, which is the energy of motion. When the gas molecules collide with the walls of the container, they transfer their kinetic energy to the container, resulting in an increase in temperature.

2. What is the role of gas pressure in heat transfer from gas to a container according to gas kinetic theory?

According to gas kinetic theory, gas pressure plays a crucial role in heat transfer from gas to a container. The pressure of a gas is directly proportional to the average kinetic energy of its molecules. Therefore, an increase in gas pressure results in an increase in the kinetic energy of gas molecules, leading to a higher rate of heat transfer to the container.

3. Can gas kinetic theory explain the different rates of heat transfer for different gases?

Yes, gas kinetic theory can explain the different rates of heat transfer for different gases. The rate of heat transfer is directly proportional to the average speed of gas molecules. Therefore, gases with higher molecular masses have slower average speeds and, consequently, lower rates of heat transfer compared to gases with lower molecular masses.

4. How does temperature affect heat transfer from gas to a container according to gas kinetic theory?

Gas kinetic theory states that an increase in temperature results in an increase in the average kinetic energy of gas molecules. This, in turn, leads to a higher rate of heat transfer from the gas to the container. Similarly, a decrease in temperature results in a decrease in the average kinetic energy and a lower rate of heat transfer.

5. Can gas kinetic theory explain the phenomenon of convection in heat transfer from gas to a container?

Yes, gas kinetic theory can explain the phenomenon of convection in heat transfer from gas to a container. Convection is the transfer of heat through the movement of fluid (in this case, gas) due to differences in temperature. Gas kinetic theory explains that the molecules of gas move faster when heated, causing them to rise and transfer heat to the cooler regions of the container. This process continues, creating a convection current and resulting in heat transfer from the gas to the container.

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