[brownsfan]

"Doesn't necessarily follow. The energy to charge the batteries has to come from somewhere."

I don't know the specifics, but I do know charging the battery isn't near the drag of running a compressor. The alternator is always "running", and a voltage regulator system decides whether the batter needs a charge or not. So, even though it's not free to charge the battery, it's close.

[coloradan]

That's because it doesn't take much power to charge a nearly-charged battery, while it takes quite a lot of power to run a compressor, or, more fundamentally, to cool the interior of the vehicle on a hot day. If you had enough Peltier devices to cool the inside, it would draw a hell of a lot more current than trickle-charging a nearly-fully-charged battery - and that would increase the torque necessary to turn the alternator by a corresponding amount.

[myself6]

The cost to charge the battery doesn't change if the battery is charging or not. The cost is paid when the belt turns the pulley that is connected to the rod that holds the windings of conductor.

Once turning, the alternator generates an electrical current. No matter the electrical load you place on the alternator the engine will NOT work harder. If the electrical load becomes to much for the alternator things will simply stop working. but the cost to run that specific alternator will not change (barring wear and tear on the bearings and sh-t like that)