# I Windmills and the second law

1. Dec 28, 2017

### Papatom

Hi,

From the movement of air molecules electricity is generated. The kinetic energy of the air molecules is converted into usefull energy and the air is cooled down.

Why do windmills not violate the second law of thermodynamics?

2. Dec 28, 2017

### Staff: Mentor

The air is not cooled down. It actually heats up a little bit. Windmills use wind, the ordered motion of air, not heat, the unordered motion of the molecules.

3. Dec 28, 2017

### Papatom

Thank you for your reply, I still do not understand this fully. Air molecules travel about 500 m/s. Assume the wind is 5 m/s. Then they have an average velocity of 505 m/s. You put a windmill somewhere and the molcules slow down to 404 m/s. Less kinetic energy so a drop in temperature. Where is my mistake?

4. Dec 28, 2017

Staff Emeritus
That's not what temperature is.

Replace wind with baseballs. Clearer?

5. Dec 28, 2017

### Staff: Mentor

No, this is not correct. If the wind is 5 m/s then the average velocity is 5 m/s. The average speed would be something like 500.03 m/s (I could be wrong on that, I think the average speed would be sqrt(500^2 + 5^2). After the windmill the average velocity will drop, but the average speed will change very little.

6. Dec 28, 2017

### A.T.

Kinetic energy is frame dependent. Temperature is related to the mean kinetic energy in the frame, where the mean velocity (bulk movement) is zero.

7. Dec 29, 2017

### Papatom

I think I understand: A plane can travel 50 m/s but the temperature indide does not increase significantly or drop after slowing down.

8. Dec 29, 2017

### cjl

Air molecules have an average velocity of around 5m/s in a 5m/s wind. In the wake of the windmill, this will be around 3m/s (velocity is directional, so the average will only be the wind speed, and will not include the thermal component). The average thermal speed of the air molecules will be basically unchanged by the windmill, so you end up with a reduction in bulk velocity and nearly zero impact on thermal speed.

EDIT: Although, from a practical standpoint, 5m/s is barely enough to get any power anyways - you'll need more like 8-10m/s before you can really do much with the wind.

9. Dec 29, 2017

### Staff: Mentor

Also, even if the wind speed were high enough that there was a significant pressure and thus temperature drop across the turbine, that still wouldn't be a drop in system entropy; you aren't looking at the whole system!