It does, all the time. The poles would be way colder and the equators so hot as to be uninhabitable otherwise. The air inside your house in your example is like the air between the poles and the equator, rushing from the cold place (the poles) to the hot place (the equator) and unlike you example, the air then rushes back again. So you have the cold air falling down and moving to the equator and the warm air rising up and moving back to the poles. Even in your example, more cold air is made at your AC and if you stand right next to it, you will still have cold air no matter if the windows are open. That’s the poles. The cold spot.
You example does work very well because the AC is weak and tiny compared to the might of the sun, so there is no balance. In the earth, though, the net heat loss at the pole is equal to the net heat gain at the equator, which is why the heat doesn’t overwhelm the cold.
If I understand it rightly, it’s always trying for an equilibrium, and always failing. Heat flows from the tropics to the poles, which is why the arctic is warming at the fastest rate on the planet. BUT – air has very little heat capacity, and air temperature is very much conditioned by the local ground or sea surface temperature. Most of the heat that reaches the planet ends up in the oceans, and it takes a very long time for heat to distribute through the water column. So ocean currents transport heat around, and where they go is shaped by continents. The Arctic, for instance, is much more open to heat inflow than the Antarctic, which is walled off to some degree by the winds and currents circling it (not entirely – as the oceans warm they eat away at Antarctic ice sheets).
Because the energy the earth recieves changes all the time. If the sun is hitting about half of the earth all the time, it’s actively warming that part up while the other half is cooling down, throw in wind, geothermal energy, tidal winds, different altitudes. You get quite a volatile heat distribution that can change rapidly
We perceive air as this uniform gas that’s just everywhere, when in reality air actually clumps around itself and forms bubbles and pockets. These bubbles form when air of the same temperature and density clump together. You’ll get bubbles of cold air, bubbles of hot air, bubbles of wet air, bubbles of dry air, etc.
In fact, wind is when these bubbles push against each other. The bubbles are so huge and so sharply determined by their heat and density and humidity, that they don’t just blend into each other: they actually form a wall, or a front, and push against each other.
You may have heard the weather forecast talking about a warm front or a cold front coming in. That’s a big bubble of one type of air pushing another. You get wind at the line where the bubbles meet, and one bubble is pushing the other.
Some airline turbulence is also caused by these bubbles, since they don’t just push around horizontally on the surface of the earth but they stack vertically on top of each other into the stratosphere, too. So sometimes when there’s turbulence or the feeling of a sudden drop while flying, it might be because the plane is punching through one air bubble into the next.
Given your example, turn on the air on one room and open all doors to the other rooms, not to the outside. The room with the AC will be cooler, right? Because while the gas which carries heat diffuses it’s not really a closed system and it’s still exchaging heat with the outside. It’s not a thermodynamically closed system.
Well Earth is the same just in a much bigger scale. Different parts recieve different amounts of heat and while it travels. Wind is caused because of the different densities / temperatures (both are related). Earth still loses heat. Also given the Albedo effect, where there is Ice like the poles, more light/heat is reflected back into space.
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