Is there a formula to determine if the amount of hydrogen generated during electrolysis outweighs the cost?

Question

Is there a mathematical formula to determine if the amount of hydrogen gas generated during electrolysis of water from a source of electricity is efficient and outweighs the energy used to produce the hydrogen gas?

An example would be: If I used a 9 volt battery sustained for 60 seconds and produced 1ml of hydrogen gas; did I acquire more energy than I used to produce the hydrogen?

Answer 1

It depends on what your paying for electricity, but a decent rule of thumb is that hydrogen costs 4 to 5 times more than other fuels. That might sound bad but if the hydrogen powers a fuel cell it could run an electric car that is 4 times more efficient than a gasoline powered car.

Answer 2

Hydrogen has 134,500 Btu/kg.

It takes about 50 kWh of electricity to manufacture one kilogram of hydrogen. One kWh is equal to 3,412 BTUs, so it takes 170,600 Btu of electricity to make 134,500 Btu of hydrogen.

Or you get back about 78% of the energy back.

Answer 3

No, you have a net decline in usable energy.  You do not need a formula to calculate this, only the second law of thermodynamics.  There is no point where the energy balance crosses over, you will always have a net loss.

Answer 4

It can only produce less power than the power used to convert the hydrogen.

If that were not true, then all you would have to do is start the process and use the hydrogen to power the hydrogen generator.

This is the same as the proverbial "perpetual motion machine".

Answer 5

The laws of thermodynamics state that you cannot create more energy that you used. You can only calculate the efficiency of electrolysis, which would be Ehydrogen/Ebattery * 100. You can't achieve 100 % efficiency because some energy is lost to heat.