# When I put my hand on a hot solid why don't the particles transfering heat to my hand exert a force on it?

When I put my hand on a hot metal (say) solid, I can feel my hand heating up. I suspect this is caused mostly by particles (electrons, atoms, ...?) from the solid colliding with the particles that make up my hand thereby transferring kinetic energy to it. But why does this lead to my hand heating up and not it (also?) being pushed?

• @R.Rankin: I'm not a physicist and I have only a very faint understanding of phonons, but my line of thinking is at the end of the day energy is transferred by particle collisions (even "within" or "across" [the interface] phonons) and I'm wondering what is the reason for these collisions sometimes leading to a pressure as in ideal gas considerations and sometimes to transfer of heat? What is the qualitative difference, the different mechanics at play? Thanks for the link! Apr 26, 2021 at 8:50
• ... to be more specific let's say "[...] sometimes to transfer of phonons" here in "[...] sometimes to transfer of heat" above. Apr 26, 2021 at 9:15
• Your hand is super heavy and your muscles apply massive force. If you were the Voyager space craft floating in a vacuum for 50 years and measuring with sensitive instruments you might notice a tiny bit of change in acceleration. Apr 26, 2021 at 9:49
• While I'd like to agree that my muscles are indeed massive, I believe my question is also valid if we consider just holding your hand against a vertical wall of the solid without applying any force at all. :) Apr 26, 2021 at 10:44
• But, if the object didn't push on your hand, your hand would go right through it.. The object must push on your hand in order to deform the surface of your skin so it forms a good contact with the surface, and transfer heat. However hard you push on the object, that is how hard it pushes on you (unless you push the wall down, or push your hand through the surface of it). Apr 27, 2021 at 7:57

Here is another scenario where the thing that you describe does happen:

A tube is filled with a gas, for example plain air. The tube fits nicely around a finger. The fit is so precise that there is a sufficient seal, so the air cannot escape, but there is only just enough friction between the tube wall and your finger to prevent the tube from sliding off just like that.

Gently increase the temperature of the gas. Now the molecules of the gas have a higher average velocity. The effect of that higher average velocity is that your finger is pushed out of the tube. The force on your finger arises from the accumulative effect of gas molecules bouncing against your skin.

A gas doesn't have internal cohesion. When you give a gas opportunity to expand it will.

Now consider a solid. A solid has internal cohesion. A solid does not expand like a gas at room temperature, and neither does it expand like a gas when you heat it up. (A solid will expand a little, but that's not visible to the naked eye.)

When you heat a solid the molecules of the solid move back and forth faster than at colder temperature. Let's say a particular molecule has - just for an instant - a velocity away from the bulk of the solid. So the molecule is on its way to ascend out of the solid. But as that molecule ascends the forces of cohesion from the neighbouring molecules increase. As a consequence the ascending molecule is pulled back into the solid.

The molecule now acquires a velocity back towards the bulk of the solid. This molecule will overshoot, and will very briefly create a local indentation of the solid.

The motion of the molecules of the solid do transfer heat to your skin as you are touching the heated solid.

And it's not just the outward punches that transfer heat. There is also an effect of interaction with the transient indentations from molecules overshooting on their way back into the bulk of the solid. You can think of that as a suction effect, if you will.

As to your skin being pushed one way or the other: the combined effect of the "punches" and the "suctions" adds to zero. What remains is the transfer of heat. For that transfer the effect of the "punches" and the "suctions" do add up; that is the transfer of heat from a solid to your skin.

• That was very helpful, thank you, especially the "sucction" part! Does that effect have a name? Apr 26, 2021 at 10:40
• @DamianBirchler It doesn't have a name, and there is no need to give it a name. The essential difference is: a solid has forces of cohesion, whereas a gas has no cohesion. If a gas molecule bounces against your finger, and pushes it back, then another gas molecule is already on its way to throw the next punch. Give a gas opportunity to expand and it will. The molecules of a solid are held back by their neighbours. In order to receive the next punch it's you who has to come back for more. (The suction narrative is sketchy, but it's funny, so I thought: "Ah, what the hell".) Apr 26, 2021 at 11:13
• Ah, but what makes me come back? The other molecules of my hand to which I as one of my hand's molecules I'm somehow connected? But if instead of my hand the hot solid is in contact with a colder gas? Will this result in a "push" of the gas away from the solid? Apr 26, 2021 at 11:19
• About the design of how stackexchange operates: the design is to not be a platform for threaded conversation. Using the comment section for threaded conversation is unpractical. If you favor opportunity to ask follow-up questions a forum with threaded conversation is better for you. That is why I'm not going into your follow-up questions. About forces between solids: you may be interested to learn about the fact that the very, very smooth surfaces of gauge blocks tend to stick together when they are brought within molecular distance to each other Apr 26, 2021 at 11:42

The important point is the question: What kind of energy is transferred to your hand.

Heat in solids is caused by vibration of the molecules and similar effects (see e.g. this question). An object can be very hot without exerting any macroscopic force, because the molecules only wiggle around instead of moving together in one direction.

When you touch a hot surface, the molecules in your hand start to wiggle as well, because the vibrations of the solid transfer to your hand. The important thing to understand here is that these vibrations cause similar vibrations in your hand, but cannot turn into macroscopic mechanical energy. This is why your hand heats up, but is not pushed.

In short: Mechanical energy and heat are both energy, but not easily turned into each other. A hot surface transfers heat to your hand, but no push. Similarly, pushing your hand would not cause it to heat up.

EDIT:
Let me elaborate on the difference between "mechanical energy" and "heat".

The over-simplified physicist model of a solid is a lattice. The atoms/molecules are connected by electric bonds which we see as elastic springs connected points next to each other:
Mechanical energy here would be the whole lattice moving in one direction. This needs a lot of energy as you need to move all atoms.
Heat in this picture corresponds to the points vibrating, i.e., moving back and forth relative to each other. Each vibration has a much lower energy because it only involves the motion of a single atom. Also, the movement is very chaotic because the atoms move in different directions.

This lattice responds very differently to different kinds of energy transfer.
To increase heat, you have to hit single atoms with a relatively high amount of energy per atom. This will cause them to vibrate.
To increase mechanical energy, you have to hit many atoms with a low amount of energy per atom.

Now lets relate this to real situations. A hot solid has strongly vibrating atoms. Putting your hand on it will transfer heat because your hand is hit by small but fast vibrating atoms.

If you close off a gas container with a piston, you'd get two situations:
With high pressure, but low temperature, the piston is hit by many gas atoms of low energy and you get mechanical energy.
With low pressure, but high energy, the piston is hit by few gas atoms of high energy and will heat up.

• Interesting, I was suspecting something like that. But from the point of view of a molecule in my hand, how is being hit by a wiggling molecule different than being hit by any other molecule, say one of a gas exerting pressure on my hand, to make the connection the answer below? What makes it behave differently than a molecule in a piston being hit by a gas molecule? Is it the "sucction" effect referred to in the below answer? Apr 26, 2021 at 10:22
• I edited my post. Does that clarify things? But you are right, I didn't account for the suction effect. Thats probably an important point! Apr 26, 2021 at 11:26
• That's very helpful, thanks. I struggled a bit at "[...] your hand is hit by small (!) but fast vibrating atoms." I would've expected "few" but fast vibrating atoms, the notion of size hasn't featured before or am I mistaken? Apr 26, 2021 at 11:40

Your hand is subject to a force, but one that operates over a microscopic distance, so its effect is not transferred to you appreciably.

Contrast the effect to that of steam escaping into a cylinder of a steam engine. The energetic water molecules impact the face of the piston within the cylinder causing the piston to move. The steam remains in contact with the face of the piston as the piston moves, continuing to exert a force on it.

By contrast, the energetic articles that comprise the hot solid are confined within the solid. Unlike the water molecules in steam they are unable to exert a force beyond a microscopic distance from the surface of the solid. Your hand would be 'pushed away' to that extent, but the distance would be a million times smaller than anything you could feel.

The force due to thermal expansion of a solid can be very significant, but it operates over a very short range.

• Interesting point about the piston's force being continuous. I'm wondering, though, what makes my hand decelerate again after being subjected, even if only very shortly, to this force mediated by colliding molecules. Apr 26, 2021 at 12:18
• It is not that your hand decelerates, but that the impulse is absorbed before it has any appreciable effect on you. By way of analogy, imagine a cushion placed on a tabletop. If you push against the cushion it will slide across the table, but only if you push it beyond a certain distance. If you push it only a millimetre or so, no matter how hard you push it, the effect of your effort is simply to distort the shape of the cushion somewhat- the cushion as a whole doesn't move. Apr 26, 2021 at 12:50
• Your argument does not make sense. If as a result of the "pushing" by the molecules in the hot body the hand were moved away far enough that no further "pushing" occurred, the heat transfer would stop as a result, which is not the case. The OP's argument is that as long as heat is transferred, some force should be felt. Apr 27, 2021 at 8:35
• Not at all. The hand makes continual contact. The push is continually made, but it is of such limited spatial extent that it does no more than influence a microscopically thin layer of the hand in contact with the solid. To return to the analogy of the cushion, you can make tiny prods to it as often as you like but it won't move. Apr 27, 2021 at 9:36

It is because the Boltzmann's constant is very small. You would need temperatures of the scale of $$10^{20}$$K to feel the push.

• Could you expand on that a bit? Are you referring to the ideal gas law here? Or to some other relation? Apr 26, 2021 at 9:13
• Yes. If I am not wrong, the equipartition theorem is quite simmilar for solids and ideal gases - it just changes some simple factor before the $k_B\cdot T$. Apr 27, 2021 at 9:42

Your hand is being pushed. If you put a hand onto the body and then suddenly heat the body up in a fraction of a second by 100 degrees, you would feel a mechanical kick into your hand. If you squeeze a body between two plates to prevent it from moving, and then heat the body up, the pressure onto the plates will increase. If you do not let the body expand upon heating, it is going to push you with all it's thermal might.

• I see your point. But in asking my question I was assuming the solid had already expanded to reflect its temperature. Apr 26, 2021 at 9:09
• Then I don't understand the question, because your hand is being pushed with the force with which you choose to push it. You choose the force, the hot body just passively counteracts it. The answer to the question "why the hot body doesn't push you" is just "because you don't choose to push it more" in this case. Apr 26, 2021 at 9:17
• But my hand will heat up which involves energy being transferred from the solid to my hand and I was wondering why this energy causes my hand's temperature to rise and not my hand being moved. In my understanding both of these outcomes constitute a "transfer of kinetic energy" (at the atomic/molecular level). And I'm wondering what makes them different. Apr 26, 2021 at 9:22
• (I'm subsuming rotational and vibrational energy under kinetic energy, here.) Apr 26, 2021 at 9:31
• Nothing... If your hand is pushed away, there is no contact anymore between the hand and the object, and therefore your hand would not be pushed away anymore. But you are constantly applying the force towards the body, and do not let your hand separate from it, so the body has constantly to push back onto your hand Apr 26, 2021 at 9:34