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First law of motion clearly says that, anything that creates a state change is a force. So, in our thermodynamic systems thermal energy, hence kinetic energy of constituent particles change when temperature is correspondingly changed. Change in kinetic energy means change in velocity, hence acceleration. So, is temperature difference here the force? Is force at its core an energy transfer/interaction?

Qmechanic
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TanfeexUlhaqq
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4 Answers4

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The first law of motion states that anything that creates a change in the rectilinear motion of a particle is a force. This is, however, only true in an inertial reference frame; in fact, this can be thought of as defining an inertial reference frame.

Temperature isn't a force, it's just a macroscopic phenomenon that has to do with microscopic forces.

Consider the following thought experiment to understand what a force is: You have an object attached to a spring whose other end is fixed and the spring-object system is in space. If you stretch the spring and release it, the spring will move the object in some manner. Now if you stick an identical object to the first and stretch the spring and release it in the same manner, the spring will move the pair of objects in some way that's different from how the spring moved the single object. Then you say to yourself "Well, the spring is pushing/pulling the objects and it seems reasonable that the strength and direction with which the string pushes/pulls doesn't depend on the objects attached to it per se, rather it depends on how stretched/compressed the spring is. I suppose that I can perhaps assign a number and direction to the push/pull of the string. Oh, and suppose I say that the first object has a quantity associated with it called its mass. Well then the second object---identical to the first---has the same mass. And let's suppose that the mass of the two objects combined is the sum of the constituent masses."

And you'd run some experiments and conclude Newton's second law: $$a \propto \frac{F}{m}\,,$$ acceleration is proportional to force divided by mass. Because the force and mass are just some numbers you pulled out of your butt, you can define the constant of proportionality to be 1 thereby making Newton's second law $$a = \frac{F}{m}\,.$$

And you say to yourself, "Well isn't that dandy?! The assumptions I made earlier are useful for computing accelerations! For if I have an object attached to my spring and it has an acceleration of 2 meters per second per second when the spring is stretched/compressed by a certain amount, I know that if I append another object identical to the first to the end of the spring, the acceleration when the spring is stretched/compressed by that same amount would be 1 meter per second per second!"

And that's my best description of what a force is; you go for the intuition and you stay for the objective, empirical results.

Energy works similarly to force: You define some fancy physical quantities to be energy (e.g. some formula involving an electric field) and it happens that if you do so you get a nice description of reality in which energy is conserved.

  • Alright I get it, how your definition of force and energy are. But my actual confusion isn't still addressed— How by increasing temperature, am I increasing the velocity of this molecule? Like how am I changing its direction by introducing a change of temperature? If it's not the temperature difference, that is doing it directly, then what is? – TanfeexUlhaqq Oct 23 '20 at 10:54
  • @TanfeexUlhaqq if you are increasing the temperature via conduction or convection in which particles carry the energy , then the high energy particles of your source collides with the low energy particles of your system and in this process the lower energy particles gain velocity. So, it is again collision which increases the temperature of the system. – Ankit Oct 23 '20 at 11:13
  • What if it's a single molecule in consideration and there's no conducting or convection. And again in order to agitate the particles of system what you need is ( let's say walls of the container, which is our system) molecules of walls to agitate. Which again happens by introducing an increment in temperature from outside, without punching the walls. The question still stands there, how are molecules of wall material agitated by temperature increment? – TanfeexUlhaqq Oct 23 '20 at 11:44
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So, is temperature difference here the force? Is force at its core an energy transfer/interaction?

Do not forget that force is a vector quantity, whereas energy is scalar. So temperature difference cannot be a force. This site might help in understanding force.

force

which for fixed mass can be seen as F=dp/dt ,

Is force at its core an energy transfer/interaction?

It is a momentum transfer interaction, and in classical mechanics connected through the size of velocity with energy.

You ask in another answer:

How by increasing temperature, am I increasing the velocity of this molecule?

Temperature is an intensive variable:

An intensive property is a bulk property, meaning that it is a local physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, T; refractive index ...

The individual particles in the material with a given temperature T do not have temperature, they have kinetic energy, and they have momentum.

You ask:

Like how am I changing its direction by introducing a change of temperature? If it's not the temperature difference, that is doing it directly, then what is?

The way temperature is related to kinetic energy in statistical mechanics

temprat

is not directly, by through the average kinetic energy of the particles in the medium studied.(the bar over the kinetic energy of the molecule means: average)

And it is the average kinetic energy that can be associated with a molecule. Heating a gas will raise its temperature , and thus the average kinetic energy, but the individual particles will be scattering randomly with various kinetic energies.

So there is a causal connection between raising the temperature and the kinetic energy of the individual molecules, but the connection is not direct, it is from a bulk property to an average of a property describing individual particles. It is not a one to one effect.

anna v
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  • "It is a momentum transfer interaction, and in classical mechanics connected through the size of velocity with energy." I cannot understand this. What does "momentum transfer interaction" mean? How is the force connected through velocity with energy? Force has no knowledge of the velocity of the object it acts on and it does not care. If it is connected with energy, it is through the work it is doing, not through velocity. – Umaxo Oct 23 '20 at 06:18
  • Did you read the link.? Acceleration is a vector, so force is a vector.. It means that it follows vector addition. The average kinetic energy of particles in a medium is an addition of scalars, The force transfers velocity to a particle,adding vectorially to the velocity of the particle. – anna v Oct 23 '20 at 06:36
  • I do not see how this addresses my questions. – Umaxo Oct 23 '20 at 07:23
  • in my answer I try to clear a misunderstanding, i.e. that force is directly related to energy transfer. it is directly related to momentum transfer. – anna v Oct 23 '20 at 07:56
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is temperature difference here the force

Force is proportional to acceleration, while temperature is function of velocities of particles, not their accelerations. This is similar to difference between force and momentum. Momentum/temperature captures the state of the system, while force captures how is this state changing. So there is big difference

Is force at its core an energy transfer

No it is not. When you have rock standing on the table, the force of gravitation is acting on it, but because it is compensated by the reaction force of the table, the rock is static and no energy transfer is happening.

Addressing the question in the comment:

How do you know that the gravitational force isn't supplying the rock with energy while the reaction force is removing energy at the same rate?

The rock in its rest frame is acted on by two forces of equal magnitudes but in opposite directions. The problem is how would you decide which of the two is supplying the energy and which one removing it? Energy, being scalar quantity, has simply too little information to address this problem.

Umaxo
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  • Somewhat tongue-in-cheek: How do you know that the gravitational force isn't supplying the rock with energy while the reaction force is removing energy at the same rate? –  Oct 23 '20 at 06:33
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    @PiKindOfGuy How would you describe the process of removing an energy? Why does one force supplies energy and the other is removing it? When rock is at rest, both forces are equivalent, just pointing in opposite directions. How do you choose which process is supplying it and which removing it? Energy has no notion of direction. You would need to raise energy from scalar quantity to some other mathematical entity that can also encode this additional information. You could perhaps do this, reformulate all of the mechanics, but in standard formulation this is simply not the case. – Umaxo Oct 23 '20 at 06:40
  • I'm a physics major, I'm just promoting a deeper explanation while messing with you. –  Oct 23 '20 at 06:44
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    @PiKindOfGuy weird flex. I understand your question, in fact I was just in the middle of addressing it in an edit. This site allows more answers at different levels and from different angles, so that reader can get broader understanding. The preferences of the readers are then handled by the voting system. – Umaxo Oct 23 '20 at 07:08
  • So answers shouldn't be downvoted if they're clearly beyond the OP's level? –  Oct 23 '20 at 07:12
  • I do not think so, no. The question and answers are for all users of the site, not just OP. This is not teaching site, where student asks the question and we are trying to explain it to him/her. This site gathers knowledge under questions, where ideally, everyone would find the answer on the level he is interested in. – Umaxo Oct 23 '20 at 07:18
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Temperature is not a force, not because it is a scalar quantity (that's like answering "because the units of measurement differ"), but because of the concept of force.

A force is a cause which effect produces spatial change of motion, evidently, change of motion of an object, as perceived by a subject. In case of temperature, objects do not change motion with temperature (in standard conditions, that is, the rock keeps being what an observer would call "the same thing" before and after the change).

Evidently, --in standard conditions-- the change of temperature of a thing changes the motion of its molecules. But that's not the movement of the thing, and that's not the change of temperature of molecules. Temperature applies to the thing, not the molecules.

In simple words, there are no "hot molecules".

RodolfoAP
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