Pressure and temperature due to frictional or momentum input

[thinkingcap81]

Hi,

I have a hypothetical question:

We have a fan which has no internal dissipation - electrical or mechanical. The fan is made to run in an adiabatically sealed room.

The internal energy of the air in the room increases due to work input. This work input increases the temperature and pressure of the air in the room.

So the question is: Is the increase in internal energy majorly due to (a) frictional effects between the fan blades and air molecules or, (b) due to momentum transfer to the air molecules?

Suppose there was no friction, then would the temperature and pressure of the air increase due to momentum transfer? If not what happens to the input work?

 

[mfb]

That depends on your fan. I would expect a reasonable fan to put more energy into bulk motion of air than into direct heat. Note that the second effect is friction as well - but this time internally in the gas (or with the walls).

 

[thinkingcap81]

That depends on your fan. I would expect a reasonable fan to put more energy into bulk motion of air than into direct heat. Note that the second effect is friction as well - but this time internally in the gas (or with the walls).

Hi,

Your explanation is what i am unclear about.

Let me limit myself to an ideal gas.

Does bulk motion of the air constitute internal energy? If so both momentum input and frictional input will cause the pressure and temperature of the air in the room to increase.

If W work is done by the fan, then does it matter how the momentum of the particles increase - whether by frictional momentum increase or simple momentum imparted even in the absence of friction?

 

[mfb]

Does bulk motion of the air constitute internal energy?

It is energy of that part of gas in the lab frame but it doesn't have an effect on its temperature at that point. The ordered kinetic energy is converted to heat later via friction.

 

[thinkingcap81]

It is energy of that part of gas in the lab frame but it doesn't have an effect on its temperature at that point. The ordered kinetic energy is converted to heat later via friction.

I made a mistake in the wordings. By bulk motion I did not mean a single velocity characterizing the entire air in the room. The temperature of an ideal gas is a measure of the mean velocity (after removing the bulk velocity of the system) of the molecules of the system. So can the fan increase the temperature due to frictional effects between the fan blades and the molecules or simple momentum transfer due to collisions of the gas molecules with the fan blades.

What is the difference between the temperature increase in the two cases: (a) frictional contribution, (b) momentum contribution.

In short i wish to understand that if we hypothetically assume that there are no frictional effects, then can temperature of the air in the room increase in the same way due to momentum transfer alone?

 

[mfb]

Different parts of the air in the room move at different velocities. Looking at the whole room as one system is misleading. Accelerating a macroscopic amount of air does not increase its temperature on its own.

 

[thinkingcap81]

Accelerating a macroscopic amount of air does not increase its temperature on its own.

I understand that. I think that we're having some miscommunication about what i wish to understand.

If there are no frictional effects between the running fan and the air molecules in the room, then can the temperature and pressure of the air increase due to collisions of the air molecules and the moving blades of the fan? After all there is electric work coming into the room via the fan.

 

[A.T.]

If there are no frictional effects between the running fan and the air molecules in the room, then can the temperature and pressure of the air increase due to collisions of the air molecules and the moving blades of the fan? After all there is electric work coming into the room via the fan.

All the energy the fan puts into the air, eventually ends up as heat. If that heat cannot escape, the temperature will rise.

 

[thinkingcap81]

All the energy the fan puts into the air, eventually ends up as heat. If that heat cannot escape, the temperature will rise.

Thank you for the reply and confirming what i thought.

My next question is: Will the temperature and pressure rise of the air in the room (with adiabatic walls) be the same with or without friction, that is, all that we need to be worried about is just what the mean kinetic energy of the molecules will be due to the work done by the fan on the air - it is immaterial whether friction+momentum transfer does it or just momentum does it.

 

[Chestermiller]

All the mechanical energy that the fan blades impart to the air causes the air in the room to move about the room, deform, and dissipate mechanical energy due to viscous dissipation. This viscous dissipation of the mechanical energy throughout the room translates into an increase in the internal energy of the air. So the specific nature of the interaction between the fan blades and the air is not nearly as important as the subsequent viscous mixing of the air throughout the bulk of the room.

 

[thinkingcap81]

All the mechanical energy that the fan blades impart to the air causes the air in the room to move about the room, deform, and dissipate mechanical energy due to viscous dissipation. This viscous dissipation of the mechanical energy throughout the room translates into an increase in the internal energy of the air. So the specific nature of the interaction between the fan blades and the air is not nearly as important as the subsequent viscous mixing of the air throughout the bulk of the room.

Right. Thanks for the explanation. More clarifications from my side:

For an ideal gas, is viscous dissipation the only way to increase internal energy? I thought that internal energy increases simply by increasing the kinetic energy of the molecules? If so, then can just momentum imparted by the fan blades can increase the internal energy? These molecules which have higher momentum can then transfer their momentum to slower moving particles and then there is an overall increase in kinetic energy.

All i am asking is that since temperature is a measure of the mean kinetic energy of the molecules, we simply need to impart more momentum to the molecules - whether this happens by friction or otherwise is immaterial.

I am thinking of a hypothetical case where there is no viscous dissipation - or is it that momentum increase of the molecules due to collisions same as viscous dissipation?

 

[Chestermiller]

Right. Thanks for the explanation. More clarifications from my side:

For an ideal gas, is viscous dissipation the only way to increase internal energy?

No. You can compress that gas or add heat to the gas. But, in a room with a fan, viscous dissipation is the only way that the final state (after the system re-equilibrates) can be one in which the gas is no longer moving bulk-wise and its temperature is higher.

I thought that internal energy increases simply by increasing the kinetic energy of the molecules? If so, then can just momentum imparted by the fan blades can increase the internal energy? These molecules which have higher momentum can then transfer their momentum to slower moving particles and then there is an overall increase in kinetic energy.

This is what viscous dissipation does. It causes the gas to become uniform with regard to specific internal energy and temperature (after the fan is shut off). Before that, the gas is non-uniform.

I am thinking of a hypothetical case where there is no viscous dissipation - or is it that momentum increase of the molecules due to collisions same as viscous dissipation?

Yes, it's the same as viscous dissipation. That is the physical mechanism associated with viscous dissipation.

 

[thinkingcap81]

No. You can compress that gas or add heat to the gas. But, in a room with a fan, viscous dissipation is the only way that the final state (after the system re-equilibrates) can be one in which the gas is no longer moving bulk-wise and its temperature is higher.

Thanks a lot for all the explanations.

About the bolded part, of course i knew it but it slipped out of my mind as i was thinking too much about the momentum transfer to the air molecules. Thanks for pointing it out.