Here’s another question I like. Peter Schmidt-Nielsen asked it to me originally. Now that I understand the answer, it feels totally trivial and I have no idea why I didn’t immediately get it, but I definitely didn’t think of the answer until like a year after he first asked me.

As a prelude, consider the following: “Air conditioners have to have a connection to the outside in order to emit the hot air they produce. Why can’t you have an air conditioner which doesn’t produce hot air?” (Many people google this, because they reasonably enough would like to purchase such a device.)

The answer to give, if you’re a smug person whose identity contains “I am very good at physics”, is, “Oh, you poor uneducated schlub. It’s because of the Second Law of Thermodynamics; every natural process in a closed system causes entropy to stay the same or increase. Cooler systems have less entropy, so if you want to keep the total entropy at least constant, you have to also heat up some air which you then expel.”

But then the questioner turns to you and says “Okay, but the system isn’t closed; you have a power cord connecting you to the outside, giving you that constant source of sweet sweet electrical power. Why can’t you transmit out the entropy through that?”

And then, if you’re anything like me, you’re like “Huh, I don’t really know, that’s a great question”, and then sit on it for a year or so until you start thinking about statistical mechanics again and then the answer is obvious.

Answer below!

. . . . .

You can totally use the power plug as the connection to the outside which you use to get rid of all the entropy you generate. But this is just saying that you’re going to heat up the power cord and let it transmit the heat away. This works, but it’s going to be a super slow way of transmitting the heat away from the air conditioner, and so your air conditioner will either have to run extremely slowly or be extremely inefficient.

Another way of thinking about this is imagining your air conditioner’s hot air tubes being connected to a small bag which also has the power cord running through it. You’re using the bag as your “hot reservoir”, and you’re using its connection to the outside via the thermal conductivity of the power cord as the mechanism by which it behaves as a reservoir (where a reservoir is something which you can put arbitrarily amount of energy into without changing its temperature).

I don’t really know why I didn’t immediately get this.

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