I am an amateur physics enthusiast, so admittedly this idea needs a lot of polishing. But it occured to me there must be a way to exploit the temperature difference between the base of a space elevator and its orbital top for power purposes. Here's what I thought up.
Taking a page of meteorology, the reason wind exists is that cold air sinks and hot air rises. As air moves away from the equator and higher into the atmosphere, it becomes colder and heavier. Similarly, as air moves toward the equator and toward the Earth's surface, it becomes hotter and lighter. This causes changes in pressure that creates the eternal loop of our planet's wind cycle.
Now, let us assume we have a space elevator. Take two large tubes (let's say about 10 feet in diameter) and run them side by side along most of the length of the elevator. Then connect them at either end and make them airtight/vacuumtight. Fill them with a stable and plentiful gas, like Nitrogen. A single element being involved will probably make the physics easier to work out.
So, we have one end of the tube sticking out into space, and the other end down near the surface of the Earth. That's a huge temperature difference. The air at the top of the tube will be extremely cold, and will want to move downward, while the hot air near the bottom will want to move upward. And as hot air move upwards, the ambient temperature will chill it, and the reverse with the cold air moving downwards.
Exaggerate this effect by implementing a valve system that only lets air pass one way through either of the tubes (one down, one up). This should create a fairly powerful wind force by manipulating the temperature differences.
Stick in wind turbines modified to work in the tube. And you have a endless power source that uses no resource other than the temperature differences created by the sun, and has no toxic side effects.
Tell me why this wouldn't work, or a way to use the same idea but better. There has to be a way to harness the temperature differences on a space ribbon for power.