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I am sorry if this question is dumb but can we apply the first law of thermodynamics directly on atoms?

I've say an ion and I'm adding an electron to it, can I write anything like $$d U=d Q-d W$$ to this process,which is related to the first law of thermodynamics?

Qmechanic
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Kashmiri
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  • Regarding your first question, a single atom has been used as a heat engine: https://physicstoday.scitation.org/doi/10.1063/PT.3.4482 – Rococo Dec 12 '20 at 06:54
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    @Rococo That's really awesome. – tryst with freedom Dec 12 '20 at 08:24
  • @Rococo the link is interesting but also conceptually misleading. In any case, it corresponds to a situation different from that in the question. – GiorgioP-DoomsdayClockIsAt-90 Dec 12 '20 at 09:51
  • @GiorgioP I'm not sure what you mean by 'conceptually misleading,' but you are correct that it is only relevant for the first question of the OP, and not the second. – Rococo Dec 12 '20 at 18:58
  • @Rococo I think it is misleading to speak about ions in electromagnetic traps using the same language of thermodynamics in a situation where most of the thermodynamics has to be heavily reinterpreted. – GiorgioP-DoomsdayClockIsAt-90 Dec 12 '20 at 22:24
  • @GiorgioP I respectfully disagree with the subjective assessment of 'heavily reinterpreted,' but I do agree that a good answer to this question (which I might try if I can find a bit of time) would elucidate the ways in which the laws of thermodynamics as applied to microscopic systems generalize the macroscopic limit. – Rococo Dec 12 '20 at 23:44
  • It would be nice to have your view as well Mr Rococo – Kashmiri Dec 14 '20 at 12:22

2 Answers2

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The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing two kinds of transfer of energy, as heat and as thermodynamic work, and relating them to a function of a body's state, called Internal energy.

italics mine.

Thermodynamics is a theory developed on the same basic laws as all of physics theories, including conservation of energy, but its variables are defined over a statistical ensembles of particles, as was made clear with the statistical form of thermodynamics..

A single atom also obeys the law of conservation of energy, but not in terms of thermodynamic variables, which apply on statistical ensembles. One atom does not make a statistical ensemble.

anna v
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  • I disagree with this answer for the case of a single atom connected to an environment, as I've elaborated in a similar question: https://physics.stackexchange.com/questions/65690/can-a-single-molecule-have-a-temperature/316596#316596 – Rococo Dec 12 '20 at 19:00
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I agree with @anna v answer.

To illustrate that thermodynamics applies to "statistical ensembles" consider the property of temperature, $T$.

The kinetic temperature of a substance is a measure of the average translational kinetic energy molecules of that substance. The speed, and thus kinetic energy, of individual molecules of a substance having a certain temperature will vary about the average. In the case of an ideal gas, the distribution of the speeds and thus kinetic energy of the molecules is given by the Maxwell Speed Distribution, as shown in the third panel of the following link: http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/kintem.html#c1

Suppose, for example, we were to remove a random sample of molecules from the ensemble, isolated it, and measure its temperature. We may find that its temperature deviates considerably from that of the ensemble because the deviation of its average kinetic energy from the ensemble. The smaller the sampling of the molecules of the ideal gas the greater the potential deviation of the average kinetic energy and "temperature" of that sample from that of the ensemble. If the sample reaches the level of a single molecule, and it happened to be a molecule having a speed corresponding to the head or tail of the Maxwell distribution, the "temperature" of that molecule would obviously have no relationship to the temperature of the ensemble of molecules.

Hope this helps.

Bob D
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  • It is true that in smaller systems fluctuations about the most probable state become increasingly important, but it is not true that when you get down to a single atom that there is no information remaining. For example, if the atom is at temperature T, then the probability of observing it with energy $10 k_BT$ is of order exp(-10), or 0.005%. Not impossible, but quite unlikely. And, if you can repeatedly monitor the atom, you can reconstruct the entire probability distribution and measure the temperature to arbitrary accuracy. – Rococo Dec 12 '20 at 19:06
  • @Rococo I never said there is no information remaining. Regarding your last statement, my example was to measure the temperature of a randomly selected sample after it is removed (isolated) from the ensemble. When the sample size becomes a single atom there will be no variation in its speed. – Bob D Dec 12 '20 at 19:56
  • @Rococo I have edited the last paragraph of my answer to clarify what I was driving at. – Bob D Dec 12 '20 at 20:16