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If there are, please provide examples. Lee Smolin suggests there are such gases in his book, "Time Reborn", but searching on my own, I could not find examples, and it seems hard to accept this is possible.

Adding the text here from the book to provide more context,

"Energy would flow from the warm side, cooling it, to the cooler side, warming it, so that soon the temperature is uniform again. Most systems work this way. But not all. Imagine there's a gas that works the other way, cooling down when you add energy to it and heating up when you take energy away. This may seem counterintuitive, but there are such gases."

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  • $\begingroup$ Are you looking for a global (ie. for all V, T, N) behavior or would you be satisfied with the inverted relationship existing for some values of V, T and N? $\endgroup$ – aidan.plenert.macdonald Jun 16 at 19:15
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I have never heard of Lee Smolin's book "Time Reborn", but yes gasses can cool down as energy is added. The first law of thermodynamics for a closed system is

$$\Delta U=Q-W$$

Where $\Delta U$ is the change in internal energy of the gas, $Q$ is the heat added to the gas (energy into the gas), and $W$ is the work done by the gas (energy out of the gas). For an ideal gas, the change in internal energy, $\Delta U$ depends only on the change in temperature and equals $C_{v}\Delta T$. So if the energy added to the gas, in the form of heat, $Q$, is less than the work done by the gas, $W$, the change in internal energy will be negative, meaning the temperature of the gas will drop (cool).

An example is the adiabatic expansion of a gas where $Q=0$. In order to envision an adiabatic expansion of a gas, think about a perfectly thermally insulated cylinder fitted with a piston. The insulation prevents any heat transfer between the gas and the surroundings. The pressure of the gas is greater than the surroundings so that it expands so that it does work. Then $\Delta U=-W$. For an adiabatic expansion $W$ is positive and therefore $\Delta U$ is negative, meaning the temperature decreases.

Hope this helps.

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  • $\begingroup$ This is helpful in terms of understanding the general case, but Smolin seemed to suggest there were specific gases where when energy was added, they would cool--and as such, I was hoping for the name of a gas in the answer. Admittedly, it is hard to imagine there are specific cases, but that is why I am asking. I am left wondering if there are gases were there's an emergent property that acts counterintuitively against the logic in your answer. Counterintuitive like water gaining volume when it freezes. $\endgroup$ – Russ Miller Jun 9 at 0:45
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    $\begingroup$ @RussMiller Just to be clear, you are saying that the NET energy into the gas is positive and yet the temperature of the gas decreases? $\endgroup$ – Bob D Jun 9 at 0:54
  • $\begingroup$ That does seem to be what Smolin is suggesting. I added a quote from the book to provide more context. $\endgroup$ – Russ Miller Jun 9 at 17:43
  • $\begingroup$ @RussMiller Now I see what Smolin is talking about. Negative specific heat. It seems to apply to stars and black holes. Take a look at the following link, in particular see John Rennie answer at the end. physics.stackexchange.com/questions/142461/…. $\endgroup$ – Bob D Jun 9 at 23:42
  • $\begingroup$ @RussMiller I think for "earthly" applications of thermodynamics we can consider specific heats as positive. $\endgroup$ – Bob D Jun 10 at 13:50
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If a volume of gas is much hotter than its surroundings, so that it is radiating heat energy faster than a smaller amount of heat energy added to it is the only way.

If any gas is at thermal equilibrium with its surroundings, adding heat energy mill raise its temperature per conservation of energy.

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With a liberal interpretation of "gas," this is one example: a globular cluster of stars bound together by gravity, where the stars are the "atoms" in this astronomically-sized "gas." This system has a negative heat capacity, which means adding more energy makes it colder. Heuristically, this is because temperature is related to the average kinetic energy of the "atoms," and adding more energy pushes the "atoms" farther away from each other (statistically speaking), which means they are moving more slowly — just like a satellite in a higher orbit moves more slowly.

For more information, see "On the negative specific heat paradox," http://adsabs.harvard.edu/full/1977MNRAS.181..405L

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    $\begingroup$ This is an interesting paradox. While not on the scale I had on my mind when asking the question, I'd upvote this if I could. Still holding out hope for the name of a specific gas (or if need be, to be told that Smolin is mistaken). $\endgroup$ – Russ Miller Jun 9 at 19:35

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