If Heat Is Motion, Why Isn’t All Motion Heat?

[sol_2001]

Homework Statement

If heat is merely molecular motion, what is the difference between a hot, stationary baseball and a cool, rapidly moving one?

Relevant Equations

No relevant equations as it is a conceptual question.

This is from the Exercises for the Feynman Lectures on Physics, Exercise 1.1. I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction. Is that correct?

 

[haruspex]

Homework Statement: If heat is merely molecular motion, what is the difference between a hot, stationary baseball and a cool, rapidly moving one?
Relevant Equations: No relevant equations as it is a conceptual question.

This is from the Exercises for the Feynman Lectures on Physics, Exercise 1.1. I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction. Is that correct?

Is that the exact wording of the question? I ask because in scientific usage "heat" only refers to the transfer of energy between bodies. Molecular motion within a body is "internal thermal energy". See e.g. https://en.wikipedia.org/wiki/Thermal_energy.
If that is the wording, your answer looks good enough.

It is interesting to consider intermediate scenarios. What about a system consisting of two balls orbiting each other? Two million balls? https://en.wikipedia.org/wiki/Maxwell's_demon

 

[Gavran]

Homework Statement: If heat is merely molecular motion, what is the difference between a hot, stationary baseball and a cool, rapidly moving one?
Relevant Equations: No relevant equations as it is a conceptual question.

This is from the Exercises for the Feynman Lectures on Physics, Exercise 1.1. I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction. Is that correct?

You ask about the difference between thermal energy and mechanical energy. Both are two different forms of kinetic energy, which is the energy of motion. All types of kinetic energy can be categorized as radiant energy, thermal energy, sound energy, electrical energy, and mechanical energy; therefore, thermal energy does not cover all forms of kinetic energy.
Mechanical energy is sometimes called “motion energy,” and this is the main reason for misunderstanding because, in this case, “motion energy,” as the other name for mechanical energy, does not capture every type of energy of motion.

 

[sol_2001]

You ask about the difference between thermal energy and mechanical energy. Both are two different forms of kinetic energy, which is the energy of motion. All types of kinetic energy can be categorized as radiant energy, thermal energy, sound energy, electrical energy, and mechanical energy; therefore, thermal energy does not cover all forms of kinetic energy.
Mechanical energy is sometimes called “motion energy,” and this is the main reason for misunderstanding because, in this case, “motion energy,” as the other name for mechanical energy, does not capture every type of energy of motion.

I should of been more specific in my definition of heat.
I know that heat is the transfer of energy from one system to another (d/t differences in temperature).
I would appreciate more of an insight into organised vs disorganised motion when it comes to the question,
however,
I do think my answer was on the right track.

 

[sol_2001]

Is that the exact wording of the question? I ask because in scientific usage "heat" only refers to the transfer of energy between bodies. Molecular motion within a body is "internal thermal energy". See e.g. https://en.wikipedia.org/wiki/Thermal_energy.
If that is the wording, your answer looks good enough.

It is interesting to consider intermediate scenarios. What about a system consisting of two balls orbiting each other? Two million balls? https://en.wikipedia.org/wiki/Maxwell's_demon

I should have been more clearer.
I know that heat is the transfer of energy from one system to another, dependant on the temperature difference, the system with a higher temperature will transfer heat to the system with a lower temperature.

 

[Herman Trivilino]

I would appreciate more of an insight into organised vs disorganised motion when it comes to the question,

You would have to give us Feynman's exact wording of the question.

 

[DaveC426913]

*Ahem*

I should of been more specific..

should have been

Careful with your diction in homework assignments.

 

[sol_2001]

*Ahem*

should have been

Careful with your diction in homework assignments.

Not a homework assignment, I'm too old for that.

 

[Lnewqban]

I would appreciate more of an insight into organized vs disorganised motion when it comes to the question,

How would you define organized and disorganized types of motion?
To me, your answer is correct.

Thermal energy is all about the frequency rate at which a group of molecules vibrate or oscillate.
Transfer of that thermal energy is all about the rate at which molecules interact or collide with other molecules located near by (think of a domino effect).

If our rapidly moving cool baseball is interacting with surrounding air, we may see transfer of thermal energy between the molecules forming the ball and the air molecules (think of the fast re-entry of space artifacts into the atmosphere).

 

[Vincf]

I don't know if that answers the question. One possible answer would be that you can convert all the kinetic energy of the "cold" ball into work, whereas you are limited in this conversion by the second law of thermodynamics if you want to use the internal energy of the "hot" ball.

 

[weirdoguy]

All types of kinetic energy can be categorized as radiant energy, thermal energy, sound energy, electrical energy, and mechanical energy;

Where did you get that from? Mechanical energy is something more than kinetic energy - it includes potential energy. Electric energy is also something different. EM radiation energy is electromagnetic energy, although I know some people call it kinetic in this context. Alpha/beta radiation energy is kinetic.

 

[256bits]

Not a homework assignment, I'm too old for that.

'Should've' sounds so much like 'should of'

 

[weirdoguy]

'Should've' sounds so much like 'should of'

Yeah, if you learn english mostly by ear, it's easy to make that mistake.

 

[Herman Trivilino]

Homework Statement: If heat is merely molecular motion, what is the difference between a hot, stationary baseball and a cool, rapidly moving one?

This is from the Exercises for the Feynman Lectures on Physics, Exercise 1.1.

A google search reveals a different exercise.

I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction. Is that correct?

Given two otherwise identical baseballs, the one with the greater internal energy will have a greater temperature regardless of their state of motion.

Heat and temperature are two fundamentally different quantities.

 

[haruspex]

Given two otherwise identical baseballs, the one with the greater internal energy will have a greater temperature regardless of their state of motion.

Heat and temperature are two fundamentally different quantities.

Leaving aside that not all internal energy is thermal, I assume that is in response to inaccuracies you see in the OP's view, namely:

I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion within the baseball, whereas a cool, fast-moving baseball has more kinetic energy due to the motion of the whole macroscopic object in a particular direction.

but I'm unclear what you object to in that.

Admittedly, there is some ambiguity. It reads as "a hot stationary ball has more thermal energy [than kinetic energy]”, etc., but more likely the intended meaning is “a hot stationary ball has more thermal energy [than a cool one]” etc.

 

[A.T.]

I would appreciate more of an insight into organised vs disorganised motion when it comes to the question,
however,

Kinetic energy of a single point particle is frame dependent, meaning that you can get rid of all of it, by adopting the rest frame of the particle.

For multiple point particles, you might not able to do that. The remaining kinetic energy, that you cannot transform away by a reference frame change, is the internal heat energy of the particle collection.

Furthermore, real world particles can have additional degrees of freedom aside from translation: rotation and deformation. The energy stored in those also counts as internal heat energy.

 

[Vincf]

As previously mentioned in this discussion, "heat" is a mode of energy transfer, and therefore the term "heat" is inappropriate. We should be talking about internal energy. Even the thermal agitation associated with a monatomic ideal gas can easily be exchanged as work with a piston.

 

[A.T.]

As previously mentioned in this discussion, "heat" is a mode of energy transfer, and therefore the term "heat" is inappropriate. We should be talking about internal energy.

"Internal energy" sounds a bit too unspecific/general to me. It sounds like all the internal energy of the object, including chemical energy and rest energy (mc^2).

I changed it to "internal heat energy" for more clarity.

 

[haruspex]

The remaining kinetic energy, that you cannot transform away by a reference frame change, is the internal heat energy of the particle collection.

Is it that clear cut? For a pair of contra-rotating discs there is a frame which minimises the KE but it is still substantial, and most of that could be used to do useful work. Seems to me there is a continuum: as the motions become less and less correlated it is progressively harder to harness the energy, ending with Maxwell's Demon.

 

[A.T.]

Is it that clear cut?

I don't think so. We often talk about macroscopic vs. microscopic kinetic energy, but this just shifts the definition to what "macroscopic" and "microscopic" is.

 

[Vincf]

In continuum mechanics, one defines a mass-specific internal energy density by
$$
e = u + \frac{1}{2}\,\rho\,v^2,
$$
where $\mathbf{v}$ is the macroscopic velocity of the material element.

The total internal energy is then :
$$
U = \int u \, dm.
$$

A sufficient separation between the macroscopic and microscopic scales is required (which is usually the case).

 

[haruspex]

I don't think so. We often talk about macroscopic vs. microscopic kinetic energy, but this just shifts the definition to what "macroscopic" and "microscopic" is.

I played with a simple one dimensional model.
Scenario 1:
Particles on a line have a uniform velocity distribution from $-V$ to $+V$.
The Shannon entropy is $-\frac 1{2V}\int_{-V}^V\frac 1{2V}log_2(\frac 1{2V}).dv=1+log_2(V)$.
The energy is $V^3/3$.

Scenario 2:
We now add the same velocity $U$ to every particle.
The energy increases but the entropy remains the same.

Scenario 3:
Instead of adding $U$ to every particle, we add $U<V$ to half and $-U$ to the rest. This leaves the mass centre of the system static.

The velocity distribution has the original density in $(-V+U, V-U)$ and half that density in $(-V-U, -V+U)$ and $(V-U, V+U)$.
The Shannon entropy is now
$-\frac{4U}{4V}log_2\frac 1{4V}-\frac{2V-2U}{2V}log_2\frac 1{2V}$
$=1+log_2V+\frac UV$
an increase of U/V.
Note that this makes sense at both U=0 and U=V since at the latter the scenario is equivalent to doubling V in scenario 1.

The energy is $\frac 13(V+U)^3$.

Scenario 4:
As scenario 1 but increasing V to V+U. This produces the same energy as scenario 3 but the entropy increase is instead $log_2(U+V)-log_2(V)=log_2(1+U/V)$.
Over the range 0<U<V, $log_2(1+U/V)>U/V$, so the entropy is lower in scenario 3 than in scenario 4. That difference represents available work.

 

[Vincf]

Am I missing something? Apart from scenario 2, in which the system is moved as a whole, are the others not practically feasible?

 

[haruspex]

Am I missing something? Apart from scenario 2, in which the system is moved as a whole, are the others not practically feasible?

I assume you mean to suggest they are infeasible sources of mechanical work.

In scenarios 1 and 4, quite so: no work can be done.
In scenario 3, nothing is specified regarding the positions of the particles. They could be two separate clouds, or maybe they will just pass through each other with few collisions.

The point is that entropy is not at its maximum in scenario 3, even though the mass centre is stationary and the system is not rotating, so in principle some work can be extracted. Consequently the available work can be more than the $\frac{(\Sigma m_i\vec v_i)^2}{2\Sigma m_i}$ implied by post #16.