This question arose when I read somewhere that adiabatic processes can only be done in thermally isolated systems and isothermal processes can only be done in thermally non-isolated system.

Now, let's just think about it: We have state functions and we can prove that some property is a state function or a path function by showing that it is an exact or inexact differential. Showing exact or inexact differential is purely mathematics. And by intuition we can show that a property is state/path function.

Now, with this perspective, we can represent every intuitive idea mathematically. Now comes my confusion:

How we can mathematically show that adiabatic processes can only occur in thermally isolated systems and isothermal process can only be done in thermally non-isolated systems?

  • $\begingroup$ @ACuriousMind , you deleted the sentence "My question is valid or not" Is my question valid ? $\endgroup$ – curious_mind Nov 24 '15 at 15:32
  • $\begingroup$ I don't understand what you mean by that. If your question doesn't make sense, you will be told anyway. I don't see what explicitly asking it adds to the question. Also, you might want to add where that "somewhere" is. $\endgroup$ – ACuriousMind Nov 24 '15 at 15:33
  • $\begingroup$ Its from my textbook of physical chemistry. It also gives the examples like thermostat(for isothermal process) and thermos flask(for adiabatic process). $\endgroup$ – curious_mind Nov 24 '15 at 15:39

From a practical standpoint, some processes can be considered adiabatic because they happen so quickly that there isn't time for any substantial heat transfer. The best common example of this is the process inside the cylinders of your auto engine when the spark plug ignites the air-fuel mixture. The resulting combustion, compression, and expansion work done on the piston as the gas expands, happens VERY quickly (e.g., on the order of 0.01 s). Admittedly, there is a small amount of energy lost as heat transfer to the engine's water jacket during this time interval, but very much smaller than the amount of expansion work being done.

  • $\begingroup$ Another example is the shock wave compression of a material. Shock wave compression is considered to be adiabatic because although the shocked material may not be thermally insulated from its surroundings, the compression occurs on such fast time scales that very little of the generated heat can escape from the material in the time scale of the compression. Shock compression, however, is not isentropic. There is a large increase in entropy when a material is shock compressed. $\endgroup$ – user93237 Nov 24 '15 at 17:55
  • $\begingroup$ So, my sentence is wrong, is it ? $\endgroup$ – curious_mind Nov 24 '15 at 23:26

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