# How do scientists know the min limit of temperature is -273 degree celsius?

How do scientists know the min limit of temperature is -273 degree celsius?

I wonder how do scientists confirmed that there is no place belong to less than -273 degree celsius in the universe? Why the scale is exactly -273 degree celsius?

• I've removed a number of comments that were attempting to answer the question and/or responses to them. Please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering.
– Chris
Nov 11, 2020 at 18:39
• I Calculated Absolute Zero With Vodka (Video answering your question) Nov 12, 2020 at 1:27

Historically the value of -273.15 C° was extrapolated from the state equation of ideal gas. In fact, theoretically (without considering quantum mechanics) at 0K° gasses would have 0 volume:

$$pV = nRT$$

Another way to calculate it is that at -273.15 (or 0K) atoms and molecules have a kinetic energy of 0, in other words they stop any movement, rotation or vibration, and since there is no way to go lower than "staying still" we can say that this is the lower limit of temperature. (In reality this is much more complicated and this is just a very simplified way to see this) Nowadays the value of -273.15 can also be retrieved considering many physical processes.

The value of 0K is demonstrated to be the lower limit of temperature and it is also demonstrated that it's impossible to reach this value. Some statistical mechanics considerations allow for "negative-temperatures" but just for small period of times, with respect to Heisenberg's uncertainty principle.

On the other hand, from a physicist point of view, you question is "wrong" since for a physicist 0K is just 0k and the "correct" question would be "why we define 0C° to be 273.15K°?". In fact the Kelvin temperature scale is based only on theoretical considerations and from "nature behaviour". The Celsius scale instead is just a convention that we use to represent the temperature.

Obviously the "width" of a Kelvin degree is also a convention, in fact in most of the application and equations you would always see the ratio of two temperatures (which is the same no matter the width of the degree you use) or you just the conversion of the temperature to energy through the Boltzmann's constant $$k_b$$.

• The Celsius scale instead is just a convention that we use to represent the temperature. - originally based on water freezing / boiling points at 1 atmosphere, so 0°C = 273.15 K came from the freezing point of water, measured in Kelvins. (Presumably we're not still adjusting what 0°C means as more accurate measurements of water temperature are made, so in that sense it's now "just convention" and defined differently, like the metre vs. earth circumference) Nov 10, 2020 at 9:50
• The negative temperatures of statistical mechanics are not colder than 0. Nov 10, 2020 at 13:14
• @PeterCordes The more important point is that "Obviously the "width" of a Kelvin degree is also a convention". An increase in temperature of 1 °C is an increase of 1 Kelvin, but not of 1 °F. Nov 10, 2020 at 14:14
• @wizzwizz4 Negative temps in stat mech are because we define temperature to be change in disorder when energy is added. Take a system of 10 2-state things with 9 units of energy. There's 9 ways to order them. Add one more unit of energy to the system and now there's only 1 way to order. If disorder goes down when energy is added, we say the temp is negative, even if those 2-state things are searing hot to the touch. Nov 10, 2020 at 20:37
• Good answer, but the fourth paragraph is distracting. The question is about absolute zero, not the relation between various conventions of representing it. Nov 11, 2020 at 21:22

The temperature of a macroscopic substance is a measure of microscopic kinetic energy of the molecules. If a sample is cooled until the molecules stop "zooming around", the temperature can be considered absolute zero. Temperature scales where the zero point of the scale corresponds to absolute zero are known as absolute temperature scales, such a Kelvin and Rankine. The Celsius and Fahrenheit temperature scales do not have their zero points set at absolute zero. For Celsius, the zero point of the scale corresponds the freezing/melting point of water (at standard pressure), and absolute zero occurs at a Celsius temperature around -273.15°. Well, theoretically. Absolute zero cannot actually be attained by any system. Even if we ignore the limitations of quantum physics (zero point energy), the inability to reach absolute zero temperature is still true in classical thermodynamics. However, it seems we can cool a system arbitrary close to absolute zero.

• @Pieter your concern would also apply to Edo98's answer, which also invokes kinetic energy. It should also be noted the question tags include Thermodynamics and do not include any Quantum-related phenomena. I would expect the tags to be an indicator of the scope of answer the OP is looking for. Nov 10, 2020 at 1:01
• Hence the quotes. Nov 10, 2020 at 1:59
• This is a good answer that is in the same register as the question. The OP doesn't appear to know that temperature is equivalent to movement and so doesn't understand that zero movement equals minimum temperature. This question clearly answers that. Insisting on quantum treatments is just nit-picking (looking at you, @Pieter...) Nov 11, 2020 at 10:15
• @Pieter Perhaps you'd care to enlighten us by crafting a better answer. Nov 11, 2020 at 19:25
• @Pieter I do so know! Temperature is atoms zooming around. It's a measure of the atomic zoomosity. Seriously,when I look at a question on SE, I try to imagine the level of understanding of the OP (i.e. the register). Then I write an answer or comment in the same register. I think that's the best way to help the OP. You might think that's condescending, and that it's better to go straight into Kerr metrics and tensor calculus. Maybe we should ask the OP what he prefers? Nov 12, 2020 at 7:53

Absolute temperature is the reciprocal of the thermodynamic $$\beta$$, coldness: $$\beta = \frac{1}{k_BT}.$$

So the short answer is that $$T=0$$ is the lowest temperature because a system cannot have $$\beta$$ higher than infinity.

It is possible to say a bit more. The thermodynamic $$\beta$$ is the logarithmic derivative of the multiplicity $$\Omega$$ (the number of accessible states of a system) with respect to the internal energy: $$\beta = \frac{1}{\Omega} \frac{{\rm d}\Omega}{{\rm d}E},$$ or $$1/k_B$$ times the derivative of entropy $$S=k_B \ln \Omega$$ which is the same thing.

A system is coldest when it is in its ground state. Then $$\Omega = 1$$ and entropy $$S=0$$. It is where the relative change of $$\Omega$$ with energy is largest. The slope of $$S$$ as a function of energy is steepest there. In macroscopic systems, the reciprocal of $$\beta$$ is essentially zero in the ground state.

Of course, historically, it was the gas laws that led to the gas temperature with a zero at $$-273\ ^\circ$$C. The Carnot efficiency then led to the thermodynamic temperature, valid not only for gases, but universal. If it were not for history, one could have used coldness instead of the Kelvin scale.

• As I might have mentioned above, I usually wince at answers that deviate too much from the register of the question. However, I do like to learn something I didn't know before, like thermodynamic coldness! This is a great answer and the inverse relation between $\beta$ and T makes the unattainability of absolute zero very clear. I only wish they hadn't called it the multiplicity of a system, though. I'd have gone for zoomosity... ;-) Nov 17, 2020 at 6:56
• “Historically, it was the gas laws that led to the gas temperature with a zero at −273”. How do scientists know, no particle in the universe has ground temperature less than -273? Nov 18, 2020 at 6:02