Can Entropy of an Ideal Gas Decrease?

[AxiomOfChoice]

Isn't it possible to come up with a transformation of an ideal gas such that $dS < 0$, 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?

 

[Vanadium 50]

No problem with decreasing the entropy of something. But you have to increase the entropy of something else.

 

[WHT]

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.

 

[krononauten]

To state what above have said:

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