So, first of all, I am a High School student and I wanted you to explain me something (in a more "concrete" way, if you know what I mean): I had an idea the other day to make a car with a wind turbine attached to it, so that the more the car runs, the more wind gets into the turbine and more energy is generated, wich powers the car. I know this is some kind of "moto perpetuo" so it wouldn't work anyway, so I asked my physics teacher about it and he said It cannot work because of the first law of thermodynamics, and he asked me a way to calculate the energy generated by the turbine. I just wanted a concrete way of showing it doesn't work, like, using data from wind turbines that exist, cars that exist and so on. But how do I calculate the energy generated?
The fundamental problem in this case is that the turbine in not powered by 'wind' as such but by the relative motion of the car through the air.
This is not 'free' energy, because the turbine must do work to generate energy it must also exert a net force opposing the motion of the car ie drag. So any energy you generate with the turbine must ultimately be provided by the car's engine.
Also no matter how well designed the turbine is some energy is wasted (second law of thermodynamics) so you will always be worse off.
Having said that there are some similar situations where you can improve the efficiency of a car with additional equipment. The difference it that, to work they much somehow harvest energy which would otherwise be wasted by the system.
One well established method is a turbocharger. This is a turbine powered not by air flowing over the body but by exhaust gasses. Conventionally turbos are used to pressurise air inducted into the engine whcih can certainly increase power and potentially improve thermal efficiency. They can also be connected to motor-generators which (in hybrid vehicles at least) can harvest electrical energy from the exhaust (see current F1 engines for more details).
Another example is regenerative braking. Here instead of using friction between brake pads and disks to slow the car down (which converts kinetic energy to heat which is lost to the surroundings) braking is achieved by using the drive train to drive a generator connected to a load (usually a battery) capable of storing energy. Again current F1 technology has used this as part of a strategy to achieve fairly spectacular improvements in thermal efficiency .
Now the turbine method you suggest could be used as a form of regenerative braking as in this case you actually want the drag from the turbine to slow the car down.
In both cases the key point is that you are harvesting energy which would otherwise be wasted and thus improving the overall efficiency of the system.
You are correct that you can't create energy by moving faster, since the only thing "wind" will do is oppose your motion.
It's certainly possible to build a vehicle which rolls on wheels and is powered either by a sail or a turbine-shaped mechanism. In fact, there's the famous (and argument-generating) design which allows a vehicle to go dead down-wind faster than the wind. See, for example, DDWFTW .
Of course, these designs are completely impracticle for on-road navigation.
I have posted some pictures and links of wind power with tires.
This vehicle proved it's possible to sail downwind faster than the wind is up for auction on Ebay.
It does work - with some limitations.
Take a sand yacht, in something like a 15mph breeze on the beam (normal to the direction of travel). As the sand yacht starts moving, the apparent wind increases and shifts forward. Sheet in, to sail close hauled. and (anecdotally) the thing accelerates like a rocket and you can be doing 50mph+ (generally with no brakes) with an apparent wind that feels almost dead ahead (you can calculate its speed and direction from simple geometry)
There is no magic involved, you are initially extracting power from the 15mph wind, and visiting a larger volume of it (tapping more available energy) when at speed.
Designing a wind turbine - which is really just a set of sails proceeding normal to the wind direction, you find the apparent wind increases as the blade starts turning - the "tip speed ratio" determines teh most efficient angle to set the blade and is often 6:1, or 90mph for the same breeze.
Limitations come with other wind directions. If the wind is dead ahead, a sail cannot extract power from it, so you would have to proceed at an angle to the actual wind. Tacking across all lanes of the highway is considered anti-social and quite possibly dangerous, unless everybody else is doing the same. This is where a wind turbine geared to drive the wheels could succeed, and again, the apparent wind sped will increase as you move to windward.
The most difficult direction, ironically, is the one you might think was easiest - with the wind dead aft. You are simply blown along, until the apparent windspeed falls towards zero. No further acceleration through this windless point is possible, though I have met someone who claimed that you could extract energy to sail downwind faster than true windspeed, provided you could sail "round" this point rather than through it. Never seen it done though...Here's one of the patents if you're interested...
Actually, it is theoretically possible to build a wind-powered vehicle. You would use a vertical windmill that can accept wind from any direction and it would charge a battery and power the vehicle's electric motor. Now of course this requires that there is wind, and that the wind creates sufficient energy to charge the battery and power the vehicle. The battery is needed for when there is not enough wind to power the vehicle. How much wind is needed and how fast one might go will require some engineering. It may turn out that there is no place with sufficient wind to overcome the losses inherent in the system. I wouldn't plan on taking the vehicle on the freeway.