Perpeptual motion and free energy

Let me start with a story.

A guy calls me up in my office (this happens sometimes). He says he wants to know if he can run a car off of hydrogen. I tell him I imagine it is possible, but it probably wouldn't work too well. Here is his plan. He wants to have the engine run an system to break water into hydrogen and oxygen. The hydrogen will then be used back in the engine. Maybe you already see the problem with this situation, but many clearly don't see the problem. Let me draw a little diagram to help.screenshot_01
So, what is wrong with this idea? Clearly there are many people that think it is a swell idea. Here are my problems:
  • First, can you run a car on hydrogen? The Mythbusters tried it, and concluded that it was not feasible. I am not a car expert, but it doesn't seem like it would work too well. But, let's pretend that it will run on hydrogen (instead of gasoline).
  • Next, at best, this would work and do nothing. Where is the energy coming from? Its coming from the hydrogen which is produced by the electrolysis which is run by the engine which is run on hydrogen (oh wait, where did I start). Theoretically, perpetual motion is possible - this does not violate the conservation of energy.
  • Finally, this neglects to include the thermodynamical limits of heat engines. There is some "energy cost" in running an engine. It is not possible for all of the energy input into the engine to be output as useful energy. That is a fundamental problem, not an engineering one. But there are engineering problems as well. The devices will never be constructed perfectly. The engine itself will not be at its peak theoretical efficiency. The electrolysis system will lose energy (thermal energy) in the wires. So, at best you can't even break even (theoretically). In reality, you can even come close to breaking even.
So, the machine proposed above is not a good idea. You will add mass to the vehicle and add more places where you can create thermal energy that you don't want. Sorry, no free lunch today.

I think there are many sites that do a much better analysis of perpetual motion machines. Here are some examples: