In the center an empty (with air) not thermally isolated room with concrete walls, floor, and ceiling, there is hanging on a non thermally conducting thread a device ("conditioner").

The weather is stable (that is the temperature outside the room does not change).

The device is equipped with a very long longevity battery.

Is it possible that (thanks to the conditioner) the temperature in the room will remain significantly (say, 3 Celsius) below the external temperature for a long time?

The essence of the question is that the conditioner cannot "suck" the heat out of the room because the device does not touch the walls or anything outside. Can a conditioner work under such restrictions?

Edit: The elements of the device cannot have very high (=infinite) heat capacity. (The only "infinitely big" thing here is the longevity of the battery.)

  • $\begingroup$ Sure, if the device consists of a cold body with very high heat capacity then this will keep the room colder than external temperature for a long time, you don't even need a battery for this... $\endgroup$ – Maxim Umansky Jun 11 '18 at 15:00
  • $\begingroup$ @MaximUmansky I want to explicitly exclude the case if it has very high heat capacity. $\endgroup$ – porton Jun 11 '18 at 15:03
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    $\begingroup$ It doesn't matter about the room insulation. You run an air conditioner by directly rejecting heat from inside the room to the outside by blowing outside air across the condenser. If the condenser is inside the room, the heat is rejected right back into the room in addition to the heat from the work to compress the refrigerant. $\endgroup$ – Chet Miller Jun 11 '18 at 17:40
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    $\begingroup$ Thermodynamics allows taking heat from one part of the room and heating up another part, if there is a thermal engine (an air-conditioner) then the part being heated can be at temperature higher than the part being cooled. So the air-conditioner can keep the room cold for some time at the expense of heating up some volume inside of the air-conditioner. Or the heat can be absorbed by a chemical reaction or phase transition of something inside the air-conditioner, e.g., melting of ice. So this can continue for some time but not indefinitely, if there is influx of external heat into the room. $\endgroup$ – Maxim Umansky Jun 11 '18 at 17:58
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    $\begingroup$ What exactly statement do we want to prove: That a part of the room can be maintained colder that the rest, as long as the air conditioner running? Or the statement that this cannot be maintained indefinitely, and as soon as the air conditioner stops the temperature in the room will start getting uniform and approaching the external temperature? $\endgroup$ – Maxim Umansky Jun 11 '18 at 18:41

This is a 1st Law question, not a 2nd Law one.

If the room is below outside ambient temperature, and not insulated, heat energy will flow into the room’s air.

That means the temperature will rise unless energy is removed from the air.

There are two things that can be done with that removed energy:

  • eject the energy from the room: you seem to have vetoed that

  • store it: you also seem to have vetoed that

So there’s no solution to removing the energy, and the temperature must rise.

The 2nd Law is about what it takes to move the energy somewhere else. But that’s not the issue until there’s somewhere to move it to...


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