[babygene]

"However, people decrease entropy all the time, an air conditioner does it, but always at the expense of doing work (using energy) and increasing entropy in the larger system."

It interesting you picked an refrigeration example. (bad choice)

They don't refer to the performance of an air conditioner in efficiency. They refer to it as "coefficient of performance". Usually it's about 400%. The reason this is "OK" is that they move heat from one place to another. They do not generate heat from some other form of energy.

[FreedomPoster]

It's a perfectly valid choice, and is exactly correct.

The local decrease in entropy in the AC system is more than offset by the increase in entropy at the power plant.

It's all in how you draw your control volume, and account for the energy flows across it.

Just because we use "real-world" measure like COP to measure the effectiveness of our mechanical creations at creating cool air, doesn't mean that the underlying thermodynamics don't adhere to the First and Second Laws.

[El Gato]

The reason this is "OK" is that they move heat from one place to another. They do not generate heat from some other form of energy.

Sure they do, more heat energy is rejected to the outside world than was removed from the air inside the house. It came from the "work" (which could be a gorilla turning a crank. :) ) needed to pump the heat "uphill" from cold to hot.