[Lewis Thomson (OP)]

Listener Jeremy would like some help finding the answers to this question,

"Considering absolute zero, is there also a maximum temperature? Perhaps an "absolute maximum" (infinite temperature)?

Given we hear temperature of exotic celestial objects measured at 10's or 100's of millions of degrees why do humans seem to inhabit a temperature range so close to absolute zero? (Or, is most of the universe actually very low temperature?)"

Leave your answers in the comments below...

[chiralSPO]

excellent questions!

I don't believe that there is any hard limit (that we know of) on the maximum possible temperature. In general, big bang energy tends to dissipate rather than concentrate, so a reasonable first approximation of the maximum temperature would be the temperature in the earliest moments of the big bang. According to this source (https://lco.global/spacebook/cosmology/early-universe/), in the first second, temperatures were on the order of 10³² Kelvin.

As a society, we are still learning about the earliest moments of the universe, so this may be subject to change.

Also, temperature can be difficult to define in extreme situations, especially if it only involves a few particles. So be aware that any discussion of "temperature" in particle collider experiments, is probably some sort of "effective temperature."

Humans are primarily made of (and dependent on) liquid water. This puts pretty significant restrictions on the range of temperatures and pressures that we can survive at. However, this apparent "specialness" is likely explained by the anthropic principle. Having arisen on the surface of the Earth, it makes sense that our existence is tuned to those conditions. I would not be terribly surprised if there were some form of plasma-based "life" that could have arisen in stars. They might not even be recognizable as alive to us (and we to them).

Finally, one thing to note is that, in some sense, negative temperatures are possible. The most common example given is lasers. https://en.wikipedia.org/wiki/Negative_temperature

[alancalverd]

Strictly speaking, if you increase the temperature of a "thing" sufficiently, it ceases to be a thing and turns into a liquid (having no defined shape it's a "stuff" rather than a "thing") then a gas, then atoms and finally plasma. The limiting temperature of plasma is the point at which all the energy of the universe, minus the mass of the thing, is invested in the ex-thing plasma.

[Bored chemist]

Strictly speaking, if you increase the temperature of a "thing" sufficiently, it ceases to be a thing and turns into a liquid (having no defined shape it's a "stuff" rather than a "thing") then a gas, then atoms and finally plasma.

Interestingly, the liquid, gas and plasma are composed of things- Ions and electrons in the case of plasma.

[alancalverd]

But temperature is not defined for an individual particle, only for a bounded ensemble.

If you want to be picky (and I'm sure some of our correspondents do) you could say that a flowing liquid or gas doesn't have a defined temperature because there will be a velocity gradient therefore a significant variance in local internal kinetic energy. Hence my preference for "stuff" rather than "thing" if the ensemble isn't bounded.

[Petrochemicals]

Depends on what constitutes temperature? Is it on atomic level or subatomic level, is the temperature considered to be on the substance in question or the measuring device. For example how could you ever measure temperature without the substance in question loosing some energy.

[Eternal Student]

Hi.

   Well I like @chiralSPO 's answer.

   There might be a limit to the amount of energy in the universe, so that would limit the temperature of a given bit of substance in the Universe.    (You could cheat and keep halving the amount of mass or substance and give that all the energy - but eventually you reach the situation @alancalverd described and you don't have enough particles to assign a temperature to the thing).

    I think there might be another practical limitation:  Hot things have fast moving particles.  We already know, from particle collider experiments, that if two particles collide you can create new particles.  Some of those collisions result in particles with more rest mass than the original particles (e.g. we can get a Higgs boson from what was assumed to be a collision of just two protons).   This removes kinetic energy from the system and converts to rest mass.  If you heat up a substance too much, it's likely to change into another substance (or more of the same substance) and oppose the temperature increase.  It's actually very common to describe the energies or velocities reached in particle colliders as the being the equivalent of seeing interactions that will occur at a particlular temperature -  @chiralSPO  mentioned this but didn't seem to make the connection.

Best Wishes.

[alancalverd]

Depends on what constitutes temperature? Is it on atomic level or subatomic level, is the temperature considered to be on the substance in question or the measuring device. For example how could you ever measure temperature without the substance in question loosing some energy.

Temperature is the mean internal kinetic energy of a mesoscopic body. It has no meaning for an individual particle.

You can in principle measure temperature without net heat loss by detecting the heat flow between the subject body at T_S and a reference at T_R. when there is no flow, T_S = T_R.

[Petrochemicals]

Depends on what constitutes temperature? Is it on atomic level or subatomic level, is the temperature considered to be on the substance in question or the measuring device. For example how could you ever measure temperature without the substance in question loosing some energy.

Temperature is the mean internal kinetic energy of a mesoscopic body. It has no meaning for an individual particle.

You can in principle measure temperature without net heat loss by detecting the heat flow between the subject body at T_S and a reference at T_R. when there is no flow, T_S = T_R.

How do you detect it if energy is not leaving the system?

[Bored chemist]

How do you detect it if energy is not leaving the system?

That's an unusually good question.
The uncertainty principle places a fundamental limit on it but at a more practical level, if I put a thermometer in my coffee, it cools the coffee and measured the temperature of the combined system.

There are a couple of ways of addressing it.
One is to use some property of the system that can be observed from "outside"- for example, I can measure the temperature changes in a metal bar if I measure changes in the length of its shadow (as projected by a constant light)

Also, I can measure the temperature of something like "melting ice" because, if I add a thermometer the temperature doesn't change; the added heat just melts ice until it is back to equilibrium.

And that's why the fixed points on the temperature scale are all phase changes.

[alancalverd]

How do you detect it if energy is not leaving the system?

When you don't detect it coming or going, it isn't transferring. Therefore the subject and the reference must be at the same temperature.

A clever way to do this (at least in principle)  is to put your sample and a small thermopile at the foci of two spherical mirrors facing one another. You heat the thermopile by passing a current through it, and measure its temperature by measuring the voltage across it when you switch off the heating current. If the sample and the thermopile are at the same temperature its voltage won't change with time immediately after switchoff.  But as I remarked elsewhere, practical heat experiments are very difficult to do!  The experiment was originally devised in response to an interview question:how would you measure the temperature of a fly?

[Bored chemist]

how would you measure the temperature of a fly?

Flir

[alancalverd]

Nowadays, yes. The question was put to undergraduates in 1963. And it still doesn't answer HY's problem of not extracting energy from the object.

[Petrochemicals]

How do you detect it if energy is not leaving the system?

When you don't detect it coming or going, it isn't transferring. Therefore the subject and the reference must be at the same temperature.

A clever way to do this (at least in principle)  is to put your sample and a small thermopile at the foci of two spherical mirrors facing one another. You heat the thermopile by passing a current through it, and measure its temperature by measuring the voltage across it when you switch off the heating current. If the sample and the thermopile are at the same temperature its voltage won't change with time immediately after switchoff.  But as I remarked elsewhere, practical heat experiments are very difficult to do!  The experiment was originally devised in response to an interview question:how would you measure the temperature of a fly?

But how do you measure a lack of transfer. I understand the principle of  lack of  register but how do you tell the temperature. All I know is two blobs are in equilibrium.

[alancalverd]

You look at the thermopile voltage and rate of change.

V α T_thermopile

dV/dt α ΔT (thermopile - fly)

[Bored chemist]

You look at the thermopile voltage and rate of change.

V α T_thermopile

dV/dt α ΔT (thermopile - fly)

If the thermopile is heating up, then it is doing so by gaining energy from the fly or whatever.
And that means the fly is cooling down.
So you are not measuring the fly, you are cooling it.
If the thermopile is cooling then you are warming the fly.

If you have a sufficient number of identical flies...

[Petrochemicals]

You look at the thermopile voltage and rate of change.

V α T_thermopile

dV/dt α ΔT (thermopile - fly)

It sounds in a similar fashion to the new fangled measurement of mass, the difference is that in the measurement of mass the system is distinct, but in the temperature measurement using a thermopile the subject and the device develop into one singular system and therefore only know the temperature of the combined singular system not the original object.

[alancalverd]

If the thermopile is heating up, then it is doing so by gaining energy from the fly or whatever.
And that means the fly is cooling down.
So you are not measuring the fly, you are cooling it.
If the thermopile is cooling then you are warming the fly.

You are beginning to see the picture.
Now what do you deduce if dV/dt = 0?

[Eternal Student]

Hi.

As @Bored chemist mentioned,    @Petrochemicals  has asked a good and challenging question, so I'm going to be on their side for a moment.

Now what do you deduce if dV/dt = 0?

   It depends on how awkward you want to be.

Simple   It shows exactly what you wanted.  The temperatures are the same.

Medium    It shows the volt meter might be broken, or similar practical problems.

Awkward    It shows the thermopile was emitting radiation at the same rate it was absorbing it.   Its temperature stays constant.  You have to be extremely careful how you get from this to deducing that the fly was at the same temperature.
   The fly was not a black body but some weird thing.   It continues radiating in much the same way, although it's temperature might be changing for a while because the radiation from the thermopile is actually heating it up, causing physical or chemical changes in the surface chitin and affecting it's emission properties.
   Obviously you can try to ensure that the fly does behave like a black body.... but you can never be sure that you have found and studied every possible way in which the fly might be transferring energy to / from the environment.   You only know that (by some mechanisms, most of which will be radiation) the fly transfers energy to the thermopile that is precisely as much energy as the thermopile emits.

Best Wishes.

[alancalverd]

The spectrum is irrelevant. As long as the source and detector are coupled and isolated from the rest of the universe, heat always and only flows from a hotter body to a cooler one.

If the voltmeter is broken it will show V = 0 all the time. I've skimped on the experimental details a bit because the thermopile needs a cold reference, but you can use ice/water if the fly is at room temperature (that's actually the answer the interviewer was looking for - it's a coldblooded creature!)  so V > 0 and over a short range, directly proportional to Celsius temperature.

There is a good reason  most flies have black bodies: optimum heat exchange to keep the enzymes working and dump waste heat from the muscles.