Why common sense is not.

When we think of common sense we think about things that intuitively make sense. They are necessarily based on what we have seen, thought or been taught before. The effects of gravity on earth make sense. The historical context of this is interesting as a force it was discovered. Before gravity common sense said that a released ball fell because there was nothing holding it up. Gravity, at least as it is seen to affect us on the planet earth is the force the pulls the ball down. We have lived as a species with the concept for so long that it is common and makes intuitive sense.  Lots of other things make sense. That heat flows from one object to another, that when you mix two vessels of air at different temperatures you get air that is the average temperature.
But there are lots of other things in our common everyday environment that are not known via sense that is common. One I learned as a child, What are the chances that in a class of 23 students some two students will have the same birthday?  It would seem that the chance me having the same birthday as you is 1/365 so with 23 students that would be 23/365. But that is not it.
Not counting the fact that there are more people born on weekends and during some seasons of the year, when you have 23 people I could have the same birthday as 22 of them. So really the number now seems like it should be 22X23/365 . This works out to a probability of over 1, more than always true. It makes no sense. The problem is more complicated than that, and I told myself I would keep math simple, intuitive for this essay. It works out to just over a 50% probability for 23 students. There is a nice wikipedia page on this: https://en.wikipedia.org/wiki/Birthday_problem
Einstein’s E=MC**2 is another example. Without an understanding of speed and satelites none of our modern navigation would work.
But for me  thermodynamic problems are both simple and counterintutive. They do not make common sense, although the sense that they do make is not so hard to understand. The basic law of thermodynamics, the first law is conservation of energy. Its been around long enough that it makes common sense. You cannot create or destroy energy. This that run contrary to this or seem to run contrary do not make common sense.
A heat exchanger is something that transfers heat from one medium to another. I like to think of these and explain them as devices that exchange air in your house with outside air. I live in Texas so I think more about airconditioning than heaters and will use a cold house for an example. Lets say that you have a kitchen exhaust fan and you cool your house to 80 degrees F and outside it is 100˚F .If you just exhaust the smokey air from your kitchen the air that sneaks into the house to replace it is 100˚F and your air conditioner will cool that down.  Its not cheap if it runs often.
So, lets say you develop a device, a metal tube with fan pushing air  outside maybe 6″  in diameter and another maybe 4″  tube placed inside it arranged with a fan to push air from outside to the inside. Just for simplicity lets say that you recover half the cooling, that the air released into the house has passed half the difference to the air going outside and they are both at 90˚F. This seems like the best you can do, it makes common sense.

But if you now place another identical device feeding air outside, and inside and place it on the inside end of your first device, coming from the outside you now have air at 90˚ and on the inside air at 80˚ so this device should do a similar thing and cool the outside air that is coming to only 85˚F . If you keep adding devices, sooner or later you get air coming in at the inside temperature and leaving at the outside temperature. If you ignore condensation you can recover nearly 100% of the coolness or if you prefer the heat. 90% efficiency is not hard to achieve for heat exchangers for the home. To really understand how these work you need calculus. But they work. Common sense would limit you  to 50%,, recovering half the heat.

Air conditioners and heat pumps are even harder to make sense of with common sense. It just is not common. These do not create heat or cool, they just move it from one place to another.

If we just used some common sense, almost no modern technology would work. If we went back to before people figured out the world was a globe we would not be able to go from Europe to Japan via New York without going back over Europe. Common sense evades sense.