Can Entropy of an Ideal Gas Decrease?

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Discussion Overview

The discussion revolves around the possibility of decreasing the entropy of an ideal gas, particularly in the context of thermodynamic transformations and phase transitions. Participants explore theoretical scenarios and implications related to entropy changes in isolated systems and the broader universe.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that it might be possible to decrease the entropy of an ideal gas by removing heat from it, questioning if dS can be less than zero.
  • Another participant acknowledges that while local decreases in entropy can occur, they assert that the overall entropy of the system must increase, implying a conservation of entropy principle.
  • A third participant introduces the idea that if enough heat is removed, a phase transition could lead to a significant decrease in informational entropy, specifically when the gas transitions to a crystalline lattice structure. However, they note that this would still require an overall increase in entropy elsewhere in the system.
  • A later reply reiterates the point that while local entropy decreases are feasible, they must be accompanied by global increases in entropy, emphasizing the second law of thermodynamics.

Areas of Agreement / Disagreement

Participants generally agree that local decreases in entropy can occur, but there is contention regarding the implications for the entire system's entropy, with no consensus on the feasibility of achieving a net decrease in entropy globally.

Contextual Notes

Participants discuss the dependence on specific conditions, such as phase transitions and the necessity of energy input, which may not be fully resolved in their arguments.

AxiomOfChoice
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Isn't it possible to come up with a transformation of an ideal gas such that [itex]dS < 0[/itex], where [itex]S[/itex] is the entropy of the gas? For example, if we remove heat [itex]dQ[/itex] from the gas (e.g., by bringing the gas into contact with a cold reservoir), doesn't that DECREASE the entropy of the gas?
 
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No problem with decreasing the entropy of something. But you have to increase the entropy of something else.
 
If enough heat was removed so that the gas happened to go through a phase transition and turn into a perfectly regularly crystalline lattice, then the informational entropy of that set of atoms or molecules would certainly drop. We could describe the order according to the equation for the lattice arrangement, which is definitely less entropy than that computed by the statistics we would use to describe the state of the gas. But as the other reply mentioned, the entropy of the entire system would have to increase as we would require energy in the form of burning fossil fuel or whatever to get the temperature to decrease.
 
To state what above have said:

Locally it is no problem decreasing the entropy (but it increases globally).
Globally it is not possible.
 

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