Entropy and Life

Natural oil (petroleum) is a mixture of many components. A well-known component of course is the gas or diesel used in our cars. A less well known component is naphtha. Naphtha is a mixture of hydrocarbon molecules that can be saturated (only single bonds between the carbon atoms) or unsaturated (double or even triple bonds between the carbon atoms. Naphtha is used as a precursor for plastics. For example the plastic poly-ethylene is a plastics that is formed when the naphtha mixture is subjected to a process called cracking (breaking up the larger molecules in smaller ones). This gives in first instance the molecule ethane that can subsequently be polymerized under formation of poly-ethylene, a plastic used in an almost endless variety range of products such as in toys, plastic garbage sacs and electrical isolation of wires. 


Because plastic is so widely used it leads at the same time also to a lot of plastic waste (plastic packaging materials, plastic bottles, toys etc). A Swiss company, Innovation Solar/Diesoil, is now doing exactly the opposite as the process described above: they have developed a process that will convert plastic waste materials into diesel fuel. 1000 kilograms of plastic will yield about 850 liter of diesel and all this at a cost price of only 26 Eurocents per liter. Recently a Dutch company (Petrogas) announced a big order to build 15 units that can turn plastic into diesel oil based on this chemical process.  


Is this not something? Sounds almost like a perpetual process…….

My question to the reader is: how will the thermodynamic balance (both energy and entropy) be for this reaction: 

Petroleum —> Plastic —>  Diesel oil

book_cover_big.gifThe human body can deliver lots of work. Consider, for instance, the athlete running a marathon, or the cyclist racing in the Tour de France. We also know that human body temperature is normally 37°C and that usually the environment is cooler, say 20°C. From this we could suggest that there is some resemblance between a heat engine, in which the body is the heat source, and the cooler environment could act as a heat sink. So let’s make a few simple calculations to see how closely the body resembles a heat engine. We know that the efficiency of a heat engine is determined by the temperatures of the heat source (the body temperature, Tbody = 310K) and the heat sink (the environmental temperature, Tsink  = 293K):

  Efficiency = [Tbody – Tsink]/Tbody = [310-293]/310 = 5.5%

 Thus, based on this temperature difference, the body would be able to achieve only 5.5% efficiency. Fortunately, scientific studies already have estimated the human body’s efficiency [1] in other ways. One study reasons that for an average man to produce 75 Watts of power, he will need to breathe about one liter of oxygen per minute. That liter of O2 is combusted in body cells to form carbon dioxide (CO2). It has also been determined that one liter of oxygen generates in this way about 300 Watts of power. Thus, we can conclude that the efficiency of the human “engine” is 75/300 = 25%. What causes the difference between the 5.5% efficiency as calculated above, and the 25% from the combustion determination? The explanation is that the human body cannot be considered a heat engine. The work is not generated in the same way as a steam engine, which directly transforms heat into work and lower-temperature waste heat. Instead, the human body is more like a fuel cell, where chemical energy is transformed into work (see also Whitt et. al.). For this kind of transformation, one obviously cannot use the efficiency formula of a heat engine.


[1] Whitt, F.R. and Wilson, D.G., Bicycling Science, MIT Press, Cambridge (1976)

book_cover_big.gifIn Part 1 (see my previous blog), I described the “food chain” and some energetic aspects of it. Now, I’d like to continue with more details and include entropic aspects as well.

Chlorophyll is the pigment in leaves that absorbs light. Typically, chlorophyll absorbs only visible light, mostly in red and blue wavelengths, and tends to reflect the green wavelength; this gives plants their familiar green color. Photosynthesis can be divided in two major steps: the oxygen-producing step (photophosphorylation) and the carbon fixation step that eventually produces glucose (also called the Calvin-Benson cycle, depicted below).

The first step, photophosphorylation, is a light-enabled reaction in which water is consumed and oxygen and molecules of adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH) are produced. To this day, we don’t completely understand all the steps and chemicals involved in making this happen. That said, we’ll limit ourselves to a brief description of how ATP and NADPH carry energy. Each molecule of ATP can store a large amount of solar energy within its chemical bonds. Likewise, an NADPH molecule can carry excited electrons, which is another way to store energy. Together, ATP and NADPH serve as the primary energy carriers in living plant cells.




A very schematic and simplified representation of the photosynthetic process. ATP, ADP, NADPH, and NADP+ are energy carriers. While photophosphorylation needs light, the Calvin‑Benson cycle can run in darkness.

The second stage (or Calvin-Benson cycle) can work without light. Using the energy of the ATP and NADPH molecules and carbon dioxide from the atmosphere, this cycle creates chemical reactions in the cell that eventually form glucose, a simple sugar.

The  overall chemical reaction of photolysis can be expressed as:

 6H2O + 6CO2 +  → C6H12O6 + 6O 

where stands for the incoming sunlight needed to drive the reaction.

On the left side are six water molecules and six carbon dioxide molecules. Altogether, they are less complex than the single sugar molecule and six oxygen molecules on the right side. Therefore, we expect the entropy to decrease during photosynthesis, which is driven by the energy in sunlight. Indeed, quantitative calculations [1] show that the entropy change for the overall reaction is negative and can be calculated as ΔS = -262 J/K (for one mole [2] of glucose, which is 180 grams). Because the entropy decreases, this reaction cannot proceed spontaneously and therefore must be driven by an external energy source – which is, of course, sunlight.

The reverse of the photosynthetic reaction occurs when the plant needs energy. This process is called “respiration of glucose,” and is in fact the combustion of glucose under well-controlled conditions in the plant cell. The products of that reaction are water and carbon dioxide, as expressed below:

C6H12O6 + 6O2 → 6H2O + 6CO2

How much energy will this reaction deliver? A lot! For example, burning 180 grams of glucose (about 40 sugar cubes) will generate almost 3000 kJ of energy – enough to allow a human weighing 75 kg (165 pounds) to climb a mountain about 4000 meters (13,200 feet) high. Impressive, isn’t it? At the molecular level, the aerobic (oxygen-based) respiration of glucose produces energy that is stored in molecules of ATP. This happens by adding a phosphate group (PO4) to ADP. Per molecule of glucose, 32 molecules of ATP are created and together they store  about 1100 kJ of energy that can be used to drive other reactions in the cell. In the case of anaerobic respiration (where little or no  oxygen is available), the energy efficiency is much less, since only two ATP molecules are formed for each combusted glucose molecule.

A sort of artificial “photosynthesis” technology is possible with photovoltaic (solar) cells. These devices use a rather elegant process to convert sunlight into electrical energy. The electrical current generated by the solar cell can then be used to split water into hydrogen and oxygen, and the resulting gases can be used in fuel cells to produce electrical power and water. On paper, this looks like a very attractive energy conversion technology, without the hazards or pollution of nuclear and fossil fuel-based power plants.

(Adapted from The Second Law of Life with permission from William Andrews Publishers)

[1] The calculation is rather simple, thanks to scientific tables that provide the standard entropy for many chemical compounds. (The term “standard” means 1 atmosphere of pressure and a temperature of  298.15 K.  The standard entropy (in J/K per mole) is 70 for (liquid) water, 214 for carbon dioxide, 205 for oxygen, and 212 for glucose. Thus, the total entropy change for the reaction without incoming sunlight works out as: ΔS = (products) – (reactants) = (212 + 6×205) – (6×214 + 6×70) = -262 J/(K mol). The decrease in entropy has to be balanced by a similar increase somewhere else in the universe. This is indeed the case, because the incoming sunlight is accompanied by an entropy increase (For instance, see W. Yourgrau and A. van der Merwe, Proc. Nat. Ac. Sci., Vol 59, p. 734 (1968). If the reaction involved water  vapor rather than liquid water, the entropy decrease would be much larger (972 J/(K mol), as the standard entropy of water vapor is 189 J/(K mol).

[2] One mole  represents  6.02 x 1023 atoms or molecules (for glucose that is 180 gram).

book_cover_big.gifAll life on earth is made possible by sunlight. We know that life needs a low-entropy resource – photosynthesis – to survive and reproduce. Utilized by plants, algae, and some bacteria, photosynthesis involves a photochemical reaction that leads eventually to a process called carbon dioxide (CO2) fixation. But before we discuss this elegant process, let’s first look at the food chain here on earth, as depicted below.




Simplified food chain. For each movement upward, the efficiency of energy utilization is only 10%. This means, for example, that humans use 10% of the available energy from the food we eat.

The principle is well known: each step in the food chain serves as nutrition for the creatures on the next step, and each animal produces carbon dioxide while consuming oxygen. What is less well known is that there is a large amount of inefficiency in this food chain. (Efficiency is defined here as the proportion of energy actually used by an organism, compared to the total energy present in its food.) This can be illustrated with several examples [Glencoe, 2004]: 100 kilograms of grain are needed to produce 10 kilograms of beef, which create only 1 kilogram of human tissue. Similarly, 3000 blades of grass are needed to produce 250 grasshoppers, which will feed 25 birds that will be eaten by just one fox. In general, each higher level in the food chain transforms only 10% of the energy from the next level beneath it. From that point of view, it is rather inefficient to feed cattle with grain, and then eat the cattle; ecologically, we would be much better off if we just ate the grain ourselves[1]. Also, energy efficiency isn’t very high in the photosynthetic process either (as we will see shortly), but the difference here is that solar energy is so abundant, photosynthetic efficiency is not a concern!

Overall, photosynthesis can be written as a chemical reaction:

6H2O + 6CO2 + hν  →  C6H12O6 + 6O2

In ordinary language, this says that six molecules of water and six molecules of carbon dioxide are transformed into one molecule of sugar and six molecules of oxygen. (The term stands for the light quanta that are needed to drive the reaction.) Massive research has shown that the fundamental chemical reactions involved in producing sugar and oxygen are the same in all photosynthetic organisms. The structure of a common sugar, β-D-glucose, is as follows:



Although the overall photosynthesis reaction suggests a rather simple mechanism, the reality is that photosynthesis is extremely complex, and even today is not completely understood. The first step in unraveling the process was Joseph Priestly’s discovery in 1770 that leafy plants produce a gas (oxygen) that supports combustion. In 1845, Julius Robert von Mayer conjectured that plants convert light energy into chemical energy.

Just a few numbers will give you a feeling for this essential life-enabling process [Whitmarsh, 1995]:

  • Producing 1 oxygen molecule requires about 8 (red [2]) light quanta. To make 180 grams of glucose, you need about 3000 kJ of energy.
  • Each year, 1014 kilograms of carbon are removed from the atmosphere by photosynthesis. The energy needed to do this represents only 0.1% of all solar energy received by the earth.
  • Every year, more than 10% of the total atmospheric carbon dioxide is converted into carbohydrates (or glucose, a 6-carbon sugar).

Pretty neat stuff , isn’t it? In Part 2, I will describe the actual photosynthetic process in a bit more detail, along with its entropy aspects. Stay tuned!

(Taken from The Second Law of Life with permission of William Andrew Publishers)

General further reading:

– Glencoe, Biology the Dynamics of Life, McGraw-Hill (2004)

– Whitmarsh J. and Govindjee; Encyclopedia of Applied Physics, Vol 13 (1995)

– Manning, Richard, “The oil we eat: following the food chain back to Iraq”, Harper’s Magazine, February (2004)


[1] A few examples to illustrate the inefficiency of the “artificial food chain” [from Manning, 2004]: The agriculture industry needs about 35 J of fossil fuel to produce one J of beef and about 68 J to produce one J of pork. Processed food requires about 10 J to produce one J of food energy.

[2] The color of the light quanta is significant, since quanta energy depends on their frequency, each of which has a characteristic color.

book_cover_big.gifThe two laws of thermodynamics (energy and entropy) have been related to the fundamental questions of the existence of life. For the finding answers to these questions several angles are possible to take. Of course we have the religious points of views. Creationists consider the First Law of thermodynamics (conservation of energy) typically as a confirmation of the ever existence of God since energy has been and will be present forever. The Second Law (increase of entropy), however, is often interpreted with a more negative flavour. The entropy law is connected to things such as decay, destruction, and chaos or disorder. There has been a lively discussion in the religious-thermodynamic realm but I prefer to come back to that discussion in another future blog. Let’s restrict ourselves for now to a more scientific treatment of the subject. For that purpose it is good to define first what the system is that we want to discuss. In thermodynamics we often work then with what is called an isolated system. Isolated means here a system that can not exchange energy, materials or anything else with its environment.


We know from the inequality of Clausius (see earlier blogs) that for an isolated system the entropy can only increase over time[1]. This is a real important statement and should be kept in the mind for the remaining part of the discussion. Have a look at the figure above. For our isolated system (the big grey box) we have, after Clausius,  ΔS >0. But for the living organism, represented by the box “Life”, we have the peculiar situation that this organism is able to keep its entropy low as is visible from the tremendous degree of order present in a living organism.

How is that done? Well the organism feeds itself on low entropy food (or energy if you wish), see also below. However, this consumption of low entropy food and from that food to built or maintain the organism structure comes with waste production (like CO2 and faeces) and also dissipation of energy into work (by the muscles) or heat (our body is able to keep us at 37°C). This is causing an entropy increase in the habitat of the organism (represented by ΔShabitat ) such that the total entropy (=ΔSlife + ΔShabitat ) ) of the isolated system increases as a whole! Erwin Schrödinger has described the feeding on low entropy energy by a living organism in his famous little book “What’s Life”[2], I can recommend to read this work. We can take this even one step further. As long as the organism is alive it is able to keep its entropy low, but when it dies this will no longer be possible and the decay and associated entropy increase starts[3]. Thus, perhaps we have here an alternative definition of living organism:

a structure that is able to keep its entropy artificially low by an intake of low entropy energy from its habitat.

If we can relate the thermodynamic laws to the fundamentals of organic life, is there then also a role for them to play in the process of natural selection? This intriguing question has been posed quite some years ago already by Alfred Lotka (1880-1949), a scientist who studied topics in the fields of popular dynamics and energetics. In 1922 he published two early articles on the relation between energy and natural selection[4],[5]. I would like to take a few interesting thoughts from his articles. Lotka regards the driving force behind natural selection as the maximization of the energy flux through the organism provided that there is still a not used residue of energy left in the system (habitat). Two, fundamentally different, categories of living species can be seen: plants which are energy accumulators (they can convert sun light into chemical energy) and animals which are basically energy engines meaning that they convert low entropy energy (stored in their food such as the plants or other animals) into high entropy (low quality) energy. According to the energy flux definition of natural selection, one could consider man as the most successful species as humans have (unconsciousness???) really mastered the “art” of maximizing or accelerating the circulation of energy and matter. However, this is only possible because of the existence of the energy accumulators, the plants!

Copyright © 2007 John E.J. Schmitz

[1] See for a more detailed discussion of this principle The Second Law of Life

[2] Erwin Schrödinger, What is life?, Cambridge University Press, London, (1951)

[3] A slightly alternative formulation of this was offered in 1921 by J. Johnstone in The Mechanism of Life: in living mechanisms the increase in entropy is retarted, see also the articles from Lotka here below

[4] A.J. Lotka, Contribution to the energetics of evolution, Proc. Natl. Acad. Sci., 8, pp 147-151 (1922)

[5] A.J. Lotka, Natural selection as a physical principle, Proc. Natl. Acad. Sci., 8, pp 151-154 (1922)