Thermodynamics of vegetation

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A greening land, A shining ether...

F. Tyutchev (1865)

On the far planet Venus, Where the gold of Sun is more flaming, Trees have blue leaves. N. Gumilev

10.1. Introduction. Energetics of photosynthesis

Organic matter in the biosphere has appeared as a result of the activity of autotrophic organisms. They represent a unique group that is able to synthesise organic matter from inorganic. While creating organic matter, they use either the energy of solar radiation (photosynthesis) or chemical energy (chemosynthesis). Photosynthesis, which is the prevailing process, produces the living biomass of vegetation, constituting 99% of the entire biomass of the biosphere. Chemosynthesis plays an important role in the nitrogen cycle and some other processes, but produces very small amounts of organic matter. Therefore, vegetation is a basic component of the biosphere and the main agent of the global biogeochemical cycles, i.e. the functioning of Biosphera machina. At the same time, photosynthesis of green plants is the main reason for the existence of all superior forms of life on our planet (and we assign ourselves to this form), since the presence of oxygen in the Earth's atmosphere is a result of photosynthesis.

The basic equation of photosynthesis is

CO2 + H2O + hv! (CH2O) + O2 + 470 kJ/mol, where hv is a photon and (CH2O) is a fragment of carbohydrate molecule. As a result of the photoreaction, 470 kJ/mol of energy is released, i.e. the change of enthalpy is AH = 470 kJ/mol. The change of free energy is equal to AG = 504 kJ/mol. Since AG = AH — TAS, the change of entropy AS is equal to (470 — 504)/293 = — 116 J/K mol (at 20°C). It is necessary to spend eight photons with total energy of about 1470 kJ/mol for the formation of one molecule of O2. Thus, the coefficient of the solar energy tapping (maximal efficiency coefficient of photosynthesis) is equal to Hmax = 504/1470 < 0.34.

Towards a Thermodynamic Theory for Ecological Systems, pp. 243-269 © 2004 Elsevier Ltd. All Rights Reserved.

We define the efficiency of photosynthesis in relation to the exergy, i.e. to the value of useful work, which can be performed by a photosynthetic system. As a result, we get a significantly lower value for the efficiency coefficient. In this case, exergy is equal to: Ex = TlASl, where lASl is the module of entropy change, lASl = 116J/Kmol, T = 293 K and Ex = 34kJ/mol. If we define the "exergetic" efficiency coefficient as Hex = Ex/Eph, where Eph = 1470 kJ/mol is the energy of photons that are necessary for photoreaction (see above), then Hex = 0.116 X 293/1470 < 0.023 = 2.3%. It is interesting that this value is almost two times lower than "the efficiency coefficient of photosynthesis for the most favourable condition", 5% (Monteith and Unsworth, 1990) and is higher than the efficiency of a "green leaf" machine, 1.68% (Section 5.3). At the same time, the efficiency coefficient for natural vegetation, defined as "the mean ratio of energy expended by the photosynthesis of natural vegetation cover to the incoming solar radiation", usually has an order of magnitude of about 0.5%. What is the reason for the differences in these estimations? This will be explained in Section 10.2.

10.2. Thermodynamic model of a vegetation layer. Fluxes of heat, water vapour and other gases

The leaves of a plant are the organs by means of which the plant assimilates carbon dioxide from the atmosphere. It, in turn, is a "case" from closed cuticle tissue pierced by multiple small holes, so-called "stomata", the size of which can be adapted to the physiological demands of the plant. A very large surface of chloroplasts with grains of chlorophyll is contained in this case. The chloroplast surface communicates with the atmosphere through stomata and intercellular space. Since carbon dioxide can only be assimilated in the soluble form, the chloroplast surface has to be humid. Hence, the humidity in the intercellular space must be very high, and it is usually much higher than the humidity of the atmosphere. Therefore, the CO2 diffusion from the atmosphere into the leaf with open stomata has to be accompanied by the diffusion of oxygen and water vapour from the leaf into the atmosphere. The latter process, which is called transpiration, is also one of the most important processes that remove metabolic heat. Another important process transporting water vapour into the atmosphere is the evaporation of water from the soil. The sum of transpiration and evaporation is called evapotranspiration. Certainly, both processes are connected with each other: evaporation influences air humidity, and the transpiration rate depends on it. Evapotranspiration maintains the difference of water potential between the atmosphere and soil that is a moving force of the flux of water from roots through leaves into the atmosphere. So, although the transpiration and evaporation are connected, but since only the transpiration affects the production process, we subdivide the system with evapotranspiration as the leading process onto the system (the transpiration and production) and its environment (the evaporation and the humidity of surrounding air).

The flux, whose intensity equals the amount of transpired water per time unit, also transports nitrogen, phosphorus, calcium, magnesium, etc. (in a soluble form), which are necessary (although in small quantities) for the formation of new biomass. This is the best illustration of one evolution principle: any organ of a living organism is multifunctional.

In consequence, the functions of vascular plants are far from the optimal. In fact, the expenditure of water resources by vegetation is very wasteful. For instance, the ratio of the increment of dry matter to the amount of evaporated water varies from 1/200 to 1/1000. Although it seems that, at first sight, such a high value of transpiration does not correspond to the physiological demands of the plant, more detailed consideration shows that there are always good reasons for such transpiration: either cooling or CO2 uptake or transport of water through the plant for the purpose of mineral uptake.

Let us consider one unit of Earth's terrestrial surface with the area As, which is covered by a certain type of natural vegetation (e.g. meadow, steppe, forest, etc.). If the vegetation cover is rather dense, then we can consider it as a single leaf (or a continuous photosynthesising media) with area A. The leaf is "packed" along the whole height of vegetation cover dv, so that the inequality A > As is fully possible. Immediately such a concept as the leaf area index L = A/As arises, so that A = LAs.

Let dj be the thickness of a leaf. Then the volume Vb occupied by the "wet" biomass of vegetation is equal to V™ = dxA = d[LAs, and the total "wet" biomass Bw = p VT = pj^diLAj where p is the density of "wet" biomass.

We assume that the transpiration is realised by some diffusion mechanism consisting of two stages. At the first stage the water vapour diffuses from the wet internal side of a leaf (the chloroplast surface) towards its external side through the stomata and intercellular space. The moving force is the gradient of concentrations of water vapour between the internal side, where the concentration Cf is close to the concentration of saturating water vapour Cw, when the leaf's temperature is T1, and the external side with concentration Cf. (For instance, if the temperature of leaves is equal to 25°C then Cf < 1.8 X 10—2gH20/g dry air.) Therefore, the water vapour flux q^ has to be proportional to the gradient of concentration, qW ~ (C^ — C^)/l1, where lj is the length of the path, along which the water vapour is moving. It is natural to assume that the length and the leaf thickness have the same order of magnitude. Without loss of generality we can assume that lj < dj. Since the transport mechanism of water vapour is diffusion, the final expression for the flux will be

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