One aspect of biological systems that intrigues students is ihc nmsihilitv of dis~:overineviolatiunsnf the well-known laws of tiermodgainics and ph&al chemistry. It is easy to refute most of the examnles suagested. A germinating seed or an embryo developing in a fertilized chicken egg are often naively cited as examules of isolated systems in which an increase in order, or decrkase in entropy occurs spontaneously. It is evident, however, that respiration, assuming 0 2 is present, produces an increase in entropy in the form of heat, which more than compensates for the decrease in entropy that arises when the elements present in the seed or in the yolk of the egg are organized into tissues of the plant or animal. Indeed, neither germination nor embryonic development will occur in the absence of oxygen in the closed system in question. The example of photosynthesis of glucose (symholized here as CH20) from CO2 and H20, in the presence of chlorophyll acting as catalyst, presents another apparent violation, hut one that is countered hy pointing out that the spectral distribution of visible light, such as sunlight, at the energy fluxes used in plant growth; implies a large free energy of the radiation field, the loss of which accounts for the decrease in entropy of the photosynthetic reaction: hu + COz + Hz0 (CHzO)+ 0% Energy conservation is always valid, and the absorption of low-entropy, highly ordered radiation more than compensates for the increase in order when carbon dioxide and water aggregate to form glucose or starch. However, this argument is not valid if this system is in thermal equilibrium. Imaeine an idealized exneriment in which a sinale chloroplast iSplaced inside a "hohlraum" at 300°K. Theradiation field is now in a state of maximum disorder. The Planck distribution of thermal energy is
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8uu2Av hu(exp(hu1kT)- 1 ) - I U.Av = -. c3
(1)
where U is the thermal energy/cm3 per Hz. Most of the radiation would lie in the infrared. How then can photosynthesis
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rrrnnr? .. ..
The ahsorption t)md of the catalyst chlun,phyll has a regiun d00 A wide centered at lilitn) A'. 1)ividing (11 hy h u gives the photon energy (lrnsits k ~ photons r 01 frequency u:
I.
(..,
Putting A = 6600A, AX = 400 A, one obtains N = m,AA = 7.10-23 photons/cm"n the red band at 300°K. The average time for absorption to occur would then be T=-
1
(Nm)
(3)
where a is the absorption cross-section of the chloroplast. For simplicity, we will assume here that the process has 100% quantum efficiency. Then u is the geometrical cross-section. This would he2: 25.10-8 cm2. Then T = 2.1018 sec, or 2.7 X 108 years. Thus, a chloroplast placed in a dark hohlraum at 300°K
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Rabinowitch, E., and Govinjee, "Photasynthesis," John Wiley & Sons,New York, 1969, p. 83, p. 131. Reference 1, Chapter 8. "eif, F., "Fundamentals of Statistical and Thermal Physics," McCraw-Hill,New York, 1965, p. 599. Fermi, E., Pasta, J., Ulam, S.,"Enrico Fermi-Collected Papers," University of Chicago Press, val. 11, paper no. 266.
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314 1 Journal of Chemical Education
containine CO?- and H?O. will after an averaae time 2.7 X lo8 years, spontaneously absorb a visible photonwandinitiate the nroduction of elucose from the simnle com~oundsH?O and CO2. This prncess involvesaderrease in entropy. A t thesame time. heat i* nhsurbed from the hohlraum radiation field.so this too loses entropy! It is evident that the entropy of the coupled system: radiation field plus chloroplast necessarily decreases in violation of the second law of thermodynamics. The violation, although quite minute, is nevertheless quite real. An objection might he raised that a chloroplast in the dark will undergo respiration, instead of photosynthesis. But this is not so. The necessary enzymes are lacking in the chloroplasts and are found only in the mitochondria of the plant. In any case the true reverse of the photosynthetic process is n
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(CHz0) + 0 2 COz + Hz0 + hu This is hioluminescence. Sugar, in the presence of oxygen and chlorophyll,should show luminescence in the red or in the blue reaion of the spectrum. I t does not. o r does it? he bioluminescence in question is just the reverse of the entropy decreasing process and could be expected to occur on a corr&nondindvlone time scale. In other words. spontaneously emits after 2.7 X los yeais, the %oro;last quantum of light, due to glucose oxidation, out into the hohlraum, where it is then degraded into the infrared. The whole Drocess restores the svstem to its oriainal state. The periodbf the "Poincare cyclei' is of the orderof 108109years in this example. The process of re-emission of light by the chloroplast occurs on a time scale like that of radioactive decay. The half-life for alpha-decay of 235Uis 7.1OS years. The radioactive uranium acts as a very weak heat source. In plant photosynthesis, occurring at thermal equilibrium, the grain of chlorophyll is a heat sinh. Photons of certain wavelengths are extracted from the environment a t the same time that an ordered structure is produced. Thus, entropy can and does decrease (and then increase) hut on a lona time scale. The possibility that svsrrms in ther~nudynamireq~~ilil)ri~lm. nuch as a O ~ I I I I ~ D I H in S ~a huhlraum at 30O0K,mny undergo large excursions.is well-known."he excursions from equilibrium that are treated in the literature generally deal with highly-idealized physical systems (ideal gases, ideal spin systems, etc.) which have the feature that the excursions are extremely short-lived. Certain biochemical systems, on the other hand, have the attribute that they may, at least in nrincinle. excursions from eauilibrium which are . .exnerience . meta-stable or lung-lived. Thus, spontaneous decrrases in entrmv iluctunt~~,t~s of remarkable ..which remesent long-lived persistence in time, may arise. Biological systems are not the only systems in which entropy oscillations can occur. In a nonlinear one-dimensional lattice containing 20 atoms, Fermi, Pasta, and Ulam4 have shown that if the energy is initially put into asingle mode (zero entropy), then as the system develops, the nonlinear coupling causes some energv to amear in the hieher modes. The entropy: -&f, log Lthereb; increases wiere f , is the fraction of enerw .."in the ith mode. However. after a sur~risinalv-short -time, the entropy decreases, and the system reverts to its initial state. Hence here too, a cyclic variation of entropy occurs.
a
