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Thermodynamics of Life

September 13, 2013

The science of thermodynamics was invented to quantify the operation of heat engines so that they might be improved. When you're stoking a steam engine, you want as much of that precious coal as possible converted into useful work.

Nearly two centuries ago, Sadi Carnot developed a simplified model of a heat engine known as a Carnot heat engine. On the basis of this model, he was able to state Carnot's theorem, that the maximum efficiency of a heat engine is a simple function of the difference in temperature between a hot reservoir (the engine) and a cold reservoir (its environment); viz,
η = 1 - (TC/TH)
where η is the efficiency, TC is the temperature of the cold reservoir, and TH is the temperature of the hot reservoir. You don't need to be a statistical mechanic to realize that a very hot engine gets near-perfect efficiency.

French physicist, Sadi CarnotFrench physicist, Nicolas Léonard Sadi Carnot (1796-1832)

Carnot's research in thermodynamics led to the later definition of entropy.

(An 1813 portrait of Carnot in school uniform at age seventeen by Louis-Léopold Boilly (1761-1845), via Wikimedia Commons.)

Real life is not that kind, so the efficiency of engines is less than 100%. Simple steam engines of the type that enabled the industrial revolution have less than 10% efficiency, with improvements such as condensers bringing that up to about 25%. Steam turbines of the type used in electrical power plants have a theoretical efficiency of about 63%, based on a steam temperature of 565°C and a condenser temperature of 35°C, but an actual efficiency of about 40%.

Standard Diesel engines have an efficiency of about 40%, which is increased to about 50% with turbo-charging. Automotive gasoline engines have efficiencies in the range of 20-30%. All that lost energy becomes waste heat, so you can see why there's research into energy harvesting from vehicle exhaust.

Living organisms are essentially specialized chemical reactors, so the laws of thermodynamics apply to them as well. Organisms maintain their order by feeding from order in the universe; that is, they generate entropy. As a consequence of the second law of thermodynamics, they also generate heat. Jeremy England, a professor of physics at the Massachusetts Institute of Technology, has just calculated the thermodynamic efficiency for replication of the simple bacterium, E. coli.[1-2]

False color image of E. coli bacteriaA false color image of E. coli bacteria.

(Via Wikimedia Commons.)

Bacteria reproduce by cell division. In the case of E. coli, this twenty minute process involves feeding, and a rearrangement of molecules such as DNA and peptides before division.[2] The key to England's calculation is the essential reversibility of thermodynamics. He looked at the reverse process of what would be needed for two cells to become one by reversing the chemical reactions of replication.[2]

The largest contributor to these reactions are 1.6 billion peptide bonds which form the basis of proteins. Calculating the bond energies gave the result that E. coli replication is an efficient process. Only six times more energy is expended than in an ideal thermodynamic system; that is, replication operates at about seventeen percent efficiency.[2] Says England,
"Given what the bacterium is made of, and given how rapidly it grows, what would be the minimum amount of heat that it would have to exhaust into its surroundings? When you compare that with the amount of heat it's actually exhausting, they're roughly on the same scale... It's relatively close to the maximum efficiency."[2]
Of course, seventeen percent is not a hundred percent. Bacteria still need to perform biological tasks other than replication. Still, there's the possibility that bacteria could be genetically engineered to grow faster, since there's nothing in principle against this.[2]

England speculates also what this finding means in the pre-biotic emergence of self-replicating nucleic acids.[1] RNA bonding is less energetic than DNA bonding, which suggests that RNA may have evolved first, since it's thermodynamically capable of replicating faster.[2]


  1. Jeremy L. England, "Statistical physics of self-replication," Journal of Chemical Physics, vol. 139, no. 12 (to appear, September 28, 2013), Document No. 121923 (8 pages).
  2. Anne Trafton, "How quickly can a bacterium grow?" MIT Press Release, August 27, 2013.
  3. England Lab Web Site at MIT.

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