Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Lewis Thomson on 12/05/2022 14:22:33
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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...
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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
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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.
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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.
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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.
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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.
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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.
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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 TS and a reference at TR. when there is no flow, TS = TR.
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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 TS and a reference at TR. when there is no flow, TS = TR.
How do you detect it if energy is not leaving the system?
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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.
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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?
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how would you measure the temperature of a fly?
Flir
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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.
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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.
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You look at the thermopile voltage and rate of change.
V α Tthermopile
dV/dt α ΔT (thermopile - fly)
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You look at the thermopile voltage and rate of change.
V α Tthermopile
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...
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You look at the thermopile voltage and rate of change.
V α Tthermopile
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.
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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?
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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.
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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.
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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.
Is the thermopile powered, thus allowing you to deduce the electron flow, or is it passive, thus meaning you do not know the temperature of it?
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Hi.
The spectrum is irrelevant.
Not if the total power emitted by the fly doesn't change at all with its temperature. Suppose it always emits 1 W of radiation regardless of the temperature of the fly.
There's no substance I know that does this exactly but that's why we were hypothesising. There could be physical and chemical changes in the outer surface of the fly depending on temperature (perhaps just changing the colour of the radiating surface from black to white and keeping total power of emissions almost constant at any temperature).
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Anyway, I'm not going to keep standing in the way. Keeping everything simple, the fly and thermopile can be assumed to be in thermal equilibrium. The forum doesn't need to confuse people with complications.
Is the thermopile powered, thus allowing you to deduce the electron flow, or is it passive, thus meaning you do not know the temperature of it?
I'm not Alancalverd but the idea seemed to be that the thermopile was powered, or somehow heated, initially to raise it to a particular temperature. Then it is switched off and can even be disconnected from any battery or circuit.
For the second part of the experiment you just connect a Volt meter to the thermopile. That's the basic idea of an idealised thermopile, it's a thing that doesn't need powering by a battery, it just generates a voltage entirely due to the temperature it has. You can measure that just by connecting a volt meter. An ideal volt meter has an infinite resistance, so we can imagine that (almost) no electrons need to flow for that measurement.
Best Wishes.
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I can't help wondering about the original question.
"Is there a limit to how hot things can get?".
I wonder if the answer is "As hot as they were".
(about 14 billion years ago)
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I can't help wondering about the original question.
"Is there a limit to how hot things can get?".
I wonder if the answer is "As hot as they were".
(about 14 billion years ago)
I believe this is correct.
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Is the thermopile powered, thus allowing you to deduce the electron flow, or is it passive, thus meaning you do not know the temperature of it?
A thermopile is a series of thermocouples. If you know the temperature of one set of junctions then the voltage across the others depends on their temperature difference - no external power involved. But if you break the circuit and inject some current you can raise the temperature of the assembly by ohmic heating. Come to think of it, I'd probably use an auxiliary heater, even simpler.
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Not if the total power emitted by the fly doesn't change at all with its temperature. Suppose it always emits 1 W of radiation regardless of the temperature of the fly.
Then you have discovered an insect that does not obey Stefan's Law, and may therefore be an alternative explanation to the Big Bang. The universe was created by a mathematical housefly!
The forum doesn't need to confuse people with complications.
That's half the fun!
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Hi.
Then you have discovered an insect that does not obey Stefan's Law,...
I'm not sure about Steafn's law. I'm familiar with the Stefan-Boltzmann law but I've only seen that proven for Black bodies. There are some things that are not black bodies.
Wikipedia uses this notation for the Stefan-Boltzmann law:
j* = total power radiated (per unit surface area) = ε.σ.T4 .
with σ = constant; T = temperature in kelvin but noteably ε = emissivity with 0 ≤ ε ≤ 1 and the following comment....
In the still more general (and realistic) case, the emissivity depends on the wavelength, ε = ε (λ).
I'm not sure what wavelength they were talking about, I guess it's the peak wavelength of the whole spectrum of emissions. Anyway, if it is that then something approximating Wien's law implies λpeak ~ 1/T. Hence, ε = ε(λ(T) ) = a function of Temperature in disguise.
So, all I'm asking is that ε(T) ~ 1/T4 over a small range of T, then the power radiated does lose all of it's dependence on T for that range of temperatures.
Best Wishes.
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In the words of any maths-for-physics lecturer: "just integrate". Time was we'd do it with a capacitor and a sweep generator, or a chart plotter, scissors and a spring balance, but I guess today's youth would use a mobile phone app, look up the answer on Google, or swoon and complain about cultural appropriation. Fact is that a good thermopile does the integration for you.
So how did we get from ionising half of the universe (the answer to the OP) to analysing the emission spectrum of a fly?
Jim Al-Khalili has a series on "size" on BBC4. His continuity advisers should study this thread!
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I'm not Alancalverd but the idea seemed to be that the thermopile was powered, or somehow heated, initially to raise it to a particular temperature. Then it is switched off and can even be disconnected from any battery or circuit.
For the second part of the experiment you just connect a Volt meter to the thermopile. That's the basic idea of an idealised thermopile, it's a thing that doesn't need powering by a battery, it just generates a voltage entirely due to the temperature it has. You can measure that just by connecting a volt meter. An ideal volt meter has an infinite resistance, so we can imagine that (almost) no electrons need to flow for that measurement.
A thermopile is a series of thermocouples. If you know the temperature of one set of junctions then the voltage across the others depends on their temperature difference - no external power involved. But if you break the circuit and inject some current you can raise the temperature of the assembly by ohmic heating. Come to think of it, I'd probably use an auxiliary heater, even simpler.
The theory of operation is then to raise the thermocouple temperature seperatley to the same and as yet unknown temperature of the object body. Connect them into one system by pure luck and register a zero voltage.
Firstly how do you know the temperature of the thermocouple if you are not withdrawing heat from it. Perhaps with another thermocouple? It would be classed as a single system
Secondly even though there is a remote possibility you may achieve equilibrium by pure chance is this really credible!
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At some point in your schooldays you should have been introduced to zero-current potentiometric measurements, the Wheatstone bridge, or some other classic null device. If not, I can only recommend that you review a basic physics text. All we are doing here is a heat-flow null using rate of change to indicate the null point.
Here's a basic aircraft instrument panel. When the dial on the lower right shows zero rate of change you are neither climbing nor descending so your lift vector equals your weight.
It is true that some physics students (and some pilots) achieve a null balance by pure chance, but most of us do it by successive approximation.
Photon coupling with mirrors is not luck.
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At some point in your schooldays you should have been introduced to zero-current potentiometric measurements, the Wheatstone bridge, or some other classic null device. If not, I can only recommend that you review a basic physics text. All we are doing here is a heat-flow null using rate of change to indicate the null point.
Here's a basic aircraft instrument panel. When the dial on the lower right shows zero rate of change you are neither climbing nor descending so your lift vector equals your weight.
It is true that some physics students (and some pilots) achieve a null balance by pure chance, but most of us do it by successive approximation.
Photon coupling with mirrors is not luck.
But the thermo couple is still not measured, unless you use a thermometer of a kind.
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You would do well to review the basic physics of thermoelectricity. Standard thermocouples and thermopiles have a known temperature coefficient of voltage. If you buy a cheapish digital multimeter it will probably come with a Type K thermocouple and thermistor compensation block that you just plug in to the meter and measure temperatures to better than ±0.1K.
Come on, PC, this is very simple, robust engineering hardware. The guy who repaired my cooker had one in his bag.
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unless you use a thermometer of a kind.
What do you think "a thermometer" means?
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You would do well to review the basic physics of thermoelectricity. Standard thermocouples and thermopiles have a known temperature coefficient of voltage. If you buy a cheapish digital multimeter it will probably come with a Type K thermocouple and thermistor compensation block that you just plug in to the meter and measure temperatures to better than ±0.1K.
Come on, PC, this is very simple, robust engineering hardware. The guy who repaired my cooker had one in his bag.
Coefficients spake greatly of powered monitoring thus allowing as you say ohmic heating. Also if you never see a change how can you be sure that your measurement is correct. You need to alter the objects temperature.
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So you always withdraw money whilst checking your bank account, because you don't believe numbers that don't change?
You do have a small point. If the vertical speed indicator doesn't fluctuate a bit, there may be a problem. Happened to a couple of chaps flying a glider in Scotland in the 1970s. They flew into falling snow but weren't panicked because the air was smooth, the wings were level, and the top right instrument (altimeter) showed a constant 1200 feet. After a few minutes it occurred to them that the airspeed indicator (top left) was reading zero, which is not good. Turned out they had grazed the top of a hill and come gently to rest in a snowdrift. Houseflies have more sense than to take to the air in a snowstorm.