What temperature actually means?

[kelvin490]

In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?

Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop?

 

[Simon Bridge]

- if you travel along with the gas it does not get hotter, but if you didn't, you could say it was hotter ... but you would more likely say it was windy.

So - yes: the T=KE(ave) is for when the container for the gas is stationary wrt the thermometer.
Same goes for the vibrating metal ... the metal is not vibrating randomly. (In practice the metal would warm up though.)

 

[kelvin490]

If a lot of gas particles travel in one direction with high speed without random motion, can we still say it has high temperature?

For other cases including solid, do we always need to take away the linear velocity every time we calculate the temperature?

 

[Simon Bridge]

I have already answered these questions.
T=KE(ave) is for when the container for the gas is stationary wrt the thermometer.
Same goes for the vibrating metal ... the metal is not vibrating randomly. (In practice the metal would warm up though.)

i.e. the answer to both questions is "no". It would be pretty unusual to include the bulk velocity with the temperature.

 

[Tom_K]

If the gas molecules are in a uniform parallel flow, with nothing to disturb them, there is no heat. If there is something to disarrange the parallelness, sending the gas molecules off on collision courses, then there would be heat.
If the solid is getting warmer then there is heat. Even though the molecular collisions are not totally random, within that non-random motion there will be disorganized non-elastic collisions, with energy being absorbed and heat is produced.

 

[rumborak]

When looking at the definition of heat through the entropy of the system, it also becomes obvious that a uniform motion won't change the entropy, and thus the heat.

 

[Jilang]

Consider ultrasonic welding. It's not the vibration directly that causes the melting and bonding. It is the friction caused by the vibration.

 

[kelvin490]

I have thought about the question again. It is no doubt that uniform motion doesn't contribute to the temperature of an object (a cup of coffee won't boil in an airplane). But for periodic motions like vibrations with high frequency and small amplitude, how does the object knows which part of its motion is random and which part is not? The motion of atoms in solid is also some sort of vibration. How to estimate temperature of a solid in such kind of motion? One may say that periodic motion is also some sort of uniform motion and won't change the entropy of the object, what if we impose irregular, random vibration to the object?

Thank you.

 

[Andy Resnick]

In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?

This is one reason why the ideal gas model is woefully inadequate to describe continuous matter. AFAIK, temperature only has a physical interpretation in connection with equilibrium. There are a few non-equilibrium thermodynamic approaches to discuss 'temperature', my preferred one is to simply use it as a primitive concept (like 'mass' in mechanics) and go from there.

 

[Khashishi]

Do we need to distinguish the random vibration KE and KE in one direction?

Yes. If you treat the ideal gas as a fluid, you need to distinguish between the velocity of a fluid element and the temperature of a fluid element. Basically, a fluid is an approximation of the gas where you don't care about the position and velocity of each gas molecule, but just the distribution function of the velocity of particles averaged over some small area. The velocity of the fluid is the mean velocity of particles. The temperature is related to the standard deviation of the velocity distribution. In general, collective group motion is not heat; it is the random motion or spread in the distribution function which is heat. Of course, collective group motion can be converted into heat, but the reverse conversion is not possible without adding extra work.

 

[sevenperforce]

I have thought about the question again. It is no doubt that uniform motion doesn't contribute to the temperature of an object (a cup of coffee won't boil in an airplane). But for periodic motions like vibrations with high frequency and small amplitude, how does the object knows which part of its motion is random and which part is not? The motion of atoms in solid is also some sort of vibration. How to estimate temperature of a solid in such kind of motion? One may say that periodic motion is also some sort of uniform motion and won't change the entropy of the object, what if we impose irregular, random vibration to the object?

Khashishi already answered this pretty well, but just to add to that:

Essentially, "heat" is the name we give to kinetic energy when it has become too disordered to directly perform any mechanical work. If you have gas that's swirling inside a cylinder, you can insert a turbine and use that to extract the kinetic energy. If you have a pendulum that's swinging back and forth with a regular period, you can hook it up to any number of mechanical devices and use that setup to extract the kinetic energy. But if all you have is random motion, then the best you can do is "dump" the random kinetic energy into a cooler region, and the amount of work you can extract from that transition is limited by the Carnot cycle.

When I was a kid, I desperately wanted to build a device which would extract work from a heat bath by using some kind of magnetic field...only to realize I was running afoul of the laws of entropy.

 

[Simon Bridge]

how does the object knows which part of its motion is random and which part is not? The motion of atoms in solid is also some sort of vibration.

It doesn't need to. Temperature is an emergent property.