Can Entropy of an Ideal Gas Decrease?

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SUMMARY

The discussion centers on the concept of entropy in ideal gases, specifically addressing the possibility of decreasing entropy (dS < 0) through heat removal (dQ) when interacting with a cold reservoir. While local entropy can decrease, such as during a phase transition to a crystalline lattice, the overall entropy of the entire system must increase due to the energy required to facilitate this process. The consensus is that while local decreases in entropy are feasible, global entropy cannot decrease.

PREREQUISITES
  • Understanding of the Second Law of Thermodynamics
  • Familiarity with concepts of entropy and phase transitions
  • Knowledge of thermodynamic systems and reservoirs
  • Basic principles of statistical mechanics
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This discussion is beneficial for physicists, thermodynamics students, and anyone interested in the principles of entropy and energy transformations in ideal gases.

AxiomOfChoice
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Isn't it possible to come up with a transformation of an ideal gas such that dS &lt; 0, where S is the entropy of the gas? For example, if we remove heat dQ 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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