Sunday, October 2, 2011

You are a Fuel Cell

"Know thyself."  Inscribed at the temple of Apollo in Delphi.

I want you to know why it's important to study fuel cells and why it's important to know how they operate. While fuel cells vehicles and fuel cell power plants are still not a major player in energy markets, and honestly, they aren't even a minor player in the energy markets, this wasn't the case roughly a hundred years ago. Fuel cell power plants used to dominate the transportation market.

The reason that fuel cells used to dominate the transportation market is that humans as well as all animal species are made up of trillions of fuel cells. Each of the mitochondria in your body is a fuel cell, capable of turning chemical exergy (i.e. sugars in the presence of oxygen) into work as well as CO2 & H2O. [In fact, some researchers have started using mitochondria in lab-scale fuel cells.] The mitochondria in animals use proton conducting membranes and concentration gradients to generate ATP from ADP and AMP. Just as in a PEM fuel cell, in order to generate work, the electrons can't travel through the proton conducting membrane, or else the electrons would short out the circuit, and no work could be generated. Instead the electrons have to travel outside of the proton conducting membrane and be consumed by oxygen molecules at the cathode along with the protons travels through the membrane to form liquid water. The electrons travel through what's called protein electron transport chains. The reaction at the cathode is the reduction of oxygen, i.e. O2+4H++4e <> 2H2O and the reaction at the anode is the oxidation of NADH, i.e. 4NADH <> 4NAD+4H++4e. The NADH was generated from sugars in the Krebs cycle.

And now, I'd like to give a quick proof that at least one reaction in a biological cell is electrochemical in nature, and not purely chemical.

Using the first and second laws of thermodynamics as well as calculating the internal generation of entropy of a chemical reaction (which goes as deltaG divided by T), one can show rather easily that the amount of work that can be generated in a chemical reaction at room temperature and pressure is exactly zero. (I will discuss more about this proof in a few paragraphs.)

So, the question is: how is it possible for a PEM fuel cell to operate at room temperature or for our mitochondria to generate the work required to lift a barbell?

The answer is that a fuel cell uses electrochemical reactions to generate power, not purely chemical reactions. You might think: well, what's the difference between a chemical and an electrochemical reaction? Both chemical and electrochemical redox reactions can occur. One difference is that, in an electrochemical reaction, electrons are forced to travel outside of the ion conducting membrane. Another difference is that chemical redox reactions can occur without electrocatalysts. Electrochemcial reactions require particular catalysts at the anode that generate electrons and catalyts at the cathode that consume electrons.

As mentioned above, the internal entropy generation is proportional to the change in the gibbs free energy of the reactants and products divided by the temperature of the reaction. This means that the exergy destruction is proportional to the change of gibbs free energy of the reactants and products times the temperature of the environment divided by the temperature of the reaction. If the temperature at which the chemical reaction occurs is the temperature of the environment, then the exergy destruction is equal to the change of the gibbs free energy of the reactants and products. This means the exergy destruction is equal to the original exergy, and hence no work will be generated.

This means that there must be some step in the multi-step chemical process that operates at a temperature much higher than room temperature. But how can any of the reactions occur at a temperature much higher than room temperature? The only way this is possible is if the temperature used in the equation for internal entropy generation of an electrochemical reaction is the energy of the "free" electrons in the electrodes divided by boltsmann's constant, which yields an effective temperature that can be over 10,000 degrees C. (On the order of the Fermi temperature of a metal.) This makes the entropy generation term extremely small. Though, all of the other temperatures used to calculate the internal generation of entropy in a room temperature fuel cell operate are room temperature. (This includes the generation of entropy via proton conduction in the membrane or the generation of entropy in the Krebs cycle away from the membrane and electrodes.)

What we are left with is a proof that living creatures have a mechanism to generate work at room temperature via the use of electrochemical reactions. This requires far-from-equilibrium thermodynamics, and we can see that fuel cells have been essential to the self-propagation of work throughout the history of life on earth. It's only been a recent phenomena that piston and turbine generation of work has dominated over the generation of work by fuel cells (i.e. animals.) Perhaps, in the future, it won't be either pistons, turbines or fuel cells that dominate the generation of work. Perhaps, one day it will be self-replicating solar cells on other planets that dominate the generation of work in our solar system.

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