Müller I. A history of thermodynamics. The doctrine of energy and entropy (1185104), страница 73
Текст из файла (страница 73)
Since theprocess occurs at constant pressure pR = 1atm and at the normal temperature,roughly TR = 298K, the first law requires that we provide heat and thesecond law demands that we withdraw heat. Indeed we haveS'J 4 ! 0by the first law, and S d 64 'U 4 0 by the second law.This is a clear contradiction and, if we did not know better, we could nowcome to the conclusion that the process is impossible.Another way to emphasize the contradiction is to calculate the change ofGibbs free energykJ'I 4 'J4 64 'U 4 2870 mol! 0.Thus the free energy grows, when we know very well that it shoulddecrease according to Gibbs, Helmholtz and every other thermodynamicistsince their time.20E.
Schrödinger: ‘‘Was ist Leben? Die lebende Zelle mit den Augen des Physikersbetrachtet.” 2nd edition. A. Francke Verlag, Bern and Leo Lehnen Verlag, München(1951).What is Life?323So there is a dilemma! The only way out seems to be to conclude that thereaction cannot occur by itself. Apart from a supply of energy there must bean accompanying process which increases the entropy far enough to offsetthe negative entropy of reaction. In fact, the increase of entropy must evenbe big enough to effect an overall decrease of Gibbs free energy.At first sight the supply of energy does not seem to present a problem,since the sun sends 1341W toward every square meter on the earth that isheld perpendicular to the incoming radiation.21 75% of that radiative powerreaches the earth’s surface and a plant leaf absorbs 65% of that, primarilythe red and yellow part of the spectrum, which is why the leaves are green.So, a leaf receives 650W/m2, and it emits the radiative power E4 C6 4 22appropriate to its temperature T.
According to plant physiologists,23 if theleaf works well at photosynthesis, each m2 may produce 1g, or 1/180 molglucose in one hour. Thus the energy balance reads650W c 4 aTm2 42789kJ11mol¹mol 1803600sm 24.3W.m2Hence follows T = 327K, or 54°C, a temperature which is high enough tolet the leaf wilt and die.
Moreover, plant physiologists inform us that photosynthesis does not work anymore beyond a temperature of 35°C.Therefore, there is a problem even with respect to the first law. A possiblekey to the solution is known to farmers, gardeners and house-wives, who allknow that a plant requires more water – much more, x-times more (say) –than dictated by the stoichiometric formula. The plant absorbs all that waterin the roots, passes it upwards to the leaves and evaporates it there. Thus aplant cools its leaves in the same manner as animals cool their skins: Byevaporation of water.24 It is easy to calculate the value of x when we requirethat the temperature stay at 298K. We obtain x § 500 so that, for each gramof water that helps to build up glucose, the plant needs to evaporate500grams to keep itself cool.2122We need to know, of course, the chemical ‘‘mechanism” by which the plant makes use ofthe radiative energy.
Biophysicist are working hard on that question and I am told thatthey have not uncovered all parts of the reaction yet, although they are getting close.E423Cequals 5.67·10–8W/m2K4, cf. Chap. 7.E.g. see W. Larcher: ‘‘Ökophysiologie der Pflanzen. Leben, Leistung undStressbewältigung der Pflanzen in ihrer Umwelt” [Ecophysiology of plants. Life,performance and stress management of plants in their environment] 5.Auflage, VerlagEugen Ulmer Stuttgart (1994).24 As far as I know, this idea was first presented by myself and A .
Klippel in the paper:A. Klippel, I. Müller: ‘‘Plant growth – a thermodynamicist’s view.” ContinuumMechanics and Thermodynamics 9, (1997).32411 MetabolismTherefore evaporation is a process accompanying photosynthesis, andthat process indeed increases entropy. However, that fact does not help withrespect to the Gibbs free energy balance, since the free energy does notchange upon evaporation. It is true that entropy grows, but the enthalpy alsogrows, such that the free energy h-Ts remains equal. So we are still lookingfor the entropy-producing accompanying process that could set the freeenergy balance right. Schrödinger made his task easy by saying:These [the plants] of course have their most powerful supply of negativeentropy in the sunlight.Let us see whether we can make sense out of this statement. We refer toChap.
7 and recall that absorption and emission of radiation by one m2 ofleaf surface produces entropy at the rate of 1.7 W/K. That amount is farbigger than the entropy increase needed for the process accompanying thephotosynthesis, which is only 0.014 W/K according to the numbers givenabove. Thus, as far as pure numbers are concerned, Schrödinger’s suggestion about the negative entropy of the sunlight could be right.
And yet, thereremains a feeling that his answer is too pat: One does not see how the leafincorporates all that entropy – or even part of it – into the chemical process.As far as I know this question has never been addressed.25All of this does not really help to answer the question ‘‘What is life?”and, although so many eminent people have failed, I should like to trymyself: Life is the indefinite working of a complex machinery. Thus eventhe steam engine, or a locomotive show traces of life.
Obviously thequestion is: How complex is complex? Surely the locomotive is too simpleto be called alive; its mechanism is too easy to understand. One is temptedto draw the analogy with art. Someone has said: If I can do it, it is not art.And so: If I can understand it, it is not life.Eventually, of course, we shall understand the working of animals andplants as well as we now understand the working of the locomotive.
Thebiophysicists and biochemists are quite successful in clearing up the livingmechanisms better and better. To be sure, they will not find life, just as littleas an engineer finds steam, when he disassembles a steam engine.25I have suggested an alternative accompanying process, – leaving out entropic radiationaltogether –, namely the mixing of the water evaporated by the leaf with the surroundingair. A. Klippel, I.
Müller: ‘‘Plant growth …” loc.cit.Name IndexAAbbott, M.M., 180Adams, H., 72,73Adams, W.S., 293Amontons, G., 5, 82Ampère, A.M., 82Andrew, T., 174, 176Arago, D.F.J., 55Aristoteles, 258Asimov, I., 12, 13, 22, 23, 30, 44, 45,47, 48, 72, 140, 152, 158, 171,198, 208, 211, 230, 237, 239, 321Au, J., 268Avogadro, A., Conte de Quaregna80, 81, 85, 86, 130, 291BBacon, F., 9Barbera, E., 269Baur, C., 15Beaumont, W., 314Becker, R., 202Belloni, L., 195Bérard, 54, 62Bergius, F.K.R., 156, 159Bergman, T.O., 152, 153Bernard, C., 314, 316Bernoulli, D., 82, 117Bernoulli, Johann 82Bernoulli, Jakob 82, 258Berthelot, P.E.M., 155, 167Berthollet, C.L., Comte de 55, 152,153Berzelius, J.J., 81, 309Bessel, F.W., 198, 293Bethe, H.A., 232Bhatnagar, P.L., 270Biot, J.B., 55Black, J., 10, 49Bohr, N.H.D., 45, 123, 212, 307Boillat, G., 258, 261, 264, 265, 300Boltzmann, L.E., 32, 64, 77, 85, 87,91–96, 99, 101–104, 106–110,118, 122, 124, 125, 142, 178, 188,190, 191, 196, 197, 200, 202, 204,207, 209, 214, 270, 274, 275, 277,300, 302Bosch, K., 157,159Bose, S.N., 100, 185, 188, 189, 192,194, 213–216Boulton, M., 49Boyle, R., 5, 82Broda, E., 107, 109Brown, R., 273Brush, S.G., 100, 185, 188, 189, 192,194, 213–216Bunsen, R.W., 198Burnett, D., 264Buys-Ballot, C.H.D., 83CCailletet, L.P., 174, 175Camus, A., 126Cantoni, G., 274Carnot, L., 52Carnot, N.L.S., 50, 52–56, 59–62,64–67, 73, 171, 236, 274Casimir, H., 249Cattaneo, C., 261–263, 266, 267Cauchy, A.L., Baron de 55, 257Cavendish, H., 309Celsius, A., 4, 6Chandrasekhar, S., 224, 295–299Chapman, S., 264Chardin, T.
de 322326IndexCharles, J.A.C., 5,82le Chatelier, W.L., 128, 156, 157Chen, P., 258Chernikov, N.A., 300, 302, 304Chevreul, M.E., 310Clapeyron, É., 52, 55, 56, 59, 61, 70Clark, A.G., 293Clarke, N.A., 284, 285Clausius, R.J.E., 28, 29, 52, 55–66,69–73, 75–77, 83, 84, 98, 103,117, 122, 146, 171, 181, 209, 243,250, 264, 269, 274Coleman, B.D., 253Compton, A.H., 45, 214, 232Comte, A., 199Cori, C.F., 317, 319Cori Radnitz, G.T., 317, 319Coriolis, G. de 55, 251, 252Cosimo III di Medici, 169Cranach, U. von, 25Crick, H.C., 313Curie, P., 247, 250Curie Sklodowska, M., 319DDalton, J., 80, 81, 129, 138Darwin, C., 110Davy, H., 12de Broglie, L., 165, 182, 183, 188,191, 289, 295Debye, P.J.W., 185Delaroche, 54, 62Demokritos, 79Denbigh, K., 124Désormes, N.G., 55Dewar, J., 24, 175, 283Dirac, P.A.M., 195Duhem, P.M.M., 76, 77, 135, 243,250, 264, 269Dulong, P.L., 16, 55Dunn, J.E., 254Dutta, M., 194, 195EEckart, C., 242, 245–247, 249, 299,302–304Eddington, A.S., 222, 226–232, 293,296Edelen, D.G.B., 252Edison, T.A., 171Ehrenfest, P., 96, 203Ehrenfest, T., 96Einstein, A., 9, 31, 33, 35–44, 110,172, 185, 188, 189, 192, 195, 197,206, 207, 209, 210–214, 227, 230,232, 275, 276–279, 300, 301, 303,304Emden, R., 224–226, 228, 230Enskog, D., 264Epicurus, 79Euler, L., 266, 267FFahrenheit, G.D., 4Faraday, M., 30, 87, 173, 174Fast, J.D., 122Fermi, E., 45, 195, 296Ferri, C., 112Fick, A., 237, 238, 240, 242, 246,278FitzGerald, G.F., 38Flory, P.J., 116Ford, H., 252Fosdick, R.L., 254Fourier, J.B.
Baron de, 55, 202, 233–236, 238, 242, 244, 246, 247,262–264, 267, 271, 286, 287, 302Franklin, B., 10Fraunhofer, J. von, 198Fresnel, A.J., 55Friedrichs, K.O., 264GGalenos, K., 1Galilei, G., 3, 10, 40, 159, 251, 256Galland, A., 159Gassendi, P., 9Gauss, C.F., 82Gay-Lussac, J.L., 5, 55, 62, 80, 81,82, 310Gentile, G., 188Georgescu-Roegen, N., 73Giauque, W.F., 185, 186IndexGibbs, J.W., 69, 71, 76, 94, 104–106,111, 117–119, 121, 122, 127–131,133, 135, 137, 138, 140, 141,146–148, 150–156, 182, 200, 206,243, 244, 245, 250, 275, 303, 304,322Giesekus, H., 250Gilbarg, D., 268Godunov, S.K., 264Goethe, J.W. von, 87, 198, 124Grad, H., 98, 268, 271, 272Green, W.A., 258Griesinger, W., 17de Groot, S.R., 247, 249, 282Gross, E.P., 270Guldberg, C.M., 153HHaber, F., 156–159Hahn, O., 44Hales, S., 308Hankel, H., 291Hasler, J., 1,2Hegel, G.W.F., 109Heisenberg, W., 44, 183, 209Helmholtz, H.L.F.
von, 13, 17, 20,24–28, 59, 73, 155, 167, 171, 209,222, 236, 295, 322van Helmont, J.B., 308Herapath, J., 82Hermann, A., 171, 209, 211Herschel, F.W., 89, 199Herschel, J., 89Hertz, H.R., 30, 211Hess, G.H., 154Hippokrates, 1Hooke, R., 9Huygens, C., 47IIngenhousz, J., 308, 309Ising, E., 121Israel, W., 300, 305JJaumann, G., 74, 245327Jeans, J.H., 203, 204, 206, 207, 213,277Joseph, D.D., 254Joule, J.P., 12–14, 16, 21–24, 26, 51,57, 59, 63, 73, 83, 117, 171, 175,179, 184, 304Jüttner, F., 289–291, 293, 295, 299,302, 305KKalisch, J., 163Kammerlingh-Onnes, H., 182Kastner, O., 121Kawashima, S., 259Kelvin, Lord, 6, 24, 30, 55, 59, 61,104, 107, 108, 117, 175, 179, 224,236, 237Kestin, J., 63Kirchhoff, G.R., 198–200, 209Klein, F., 108Klein, M.J., 108Klippel, A., 323, 324Krebs, H.A., 315, 316, 319Krönig, A.K., 83Krook, M., 270Kuhn, T.S., 57Kuhn, W., 113, 116Kurlbaum, F., 205LLagrange, J.L. Comte de, 55, 79,132, 134, 257, 260, 264, 265Lamé, G., 55Landau, L.D., 183–185Landsberg, P.T., 305Lane, J.H., 224–226, 228, 230Langevin, P., 279Laplace, P.S.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
