Entropy and Entropy Flows in the Biosphere

Abstract

From a thermodynamic point of view, Earth is a closed system, which gets 238 W m −2 of energy from the Sun in the form of a short-wave radiation. The same amount of energy is irradiated into the space in the form of a long-wave (infrared) radiation. Since the Earth’s surface + atmosphere system (EAS) is not significantly changed during the last millenaries, the statements that it is at the dynamic equilibrium and, in accordance with Prigogine’s theorem, that its internal entropy production is balanced by the exchange entropic flow d e σ / dt = − 1.2 WK − 1 m − 2 , or −2 × 10 22 J K −1 yr −1 for the globe overall are true. It is interesting that both d e σ G /d t ≈ −0.586 W K −1 m −2 for the ground and d e σ A /d t ≈ −0.576 W K −1 m −2 for the atmosphere are almost equal. Their negativeness means that both atmosphere and Earth’s surface can perform some work. A living film partially covering the Earth’s surface, the biota, is rather interesting for us. The equation of its entropy balance is d S B / d t ≈ [ ( 0.53 − 4.11 ) × 10 20 = − 3.58 × 10 20 JK − 1 yr − 1 ] + S ⋅ Work B , that is, from the thermodynamic point of view, biota is a strongly nonequilibrium system, which is able to perform some useful work (S˙ Work B is the entropy produced by the biota during its work). Since the biota is at the equilibrium, d S B /d t = 0, and S˙ Work B = 3.58×10 20 J K −1 yr −1 . What is the origin of this value? We shall use the exergy concept, since exergy is a measure of the system’s ability of performing the work, which is an upper bound for the ‘useless’ work. In accordance with the concept, exergy = β h DOM ·NPP, where h DOM = 17.4 kJ g −1 is the specific enthalpy of one gram of dead organic matter in dry weight (d.w.). The NPP is the net primary production, 1.4 × 10 17 g d.w., and β is some species-specific factor determined by the length of genome of the corresponding living individual (in our case this is the terrestrial vegetation with β ∈ [29, 87]). The zero balance is attained at β ≈ 42. This approach allows us to get some estimation of the limit of anthropogenic loads on the biosphere. For instance, the lower bound of β is β * = 29, which is equivalent to full disappearance of vascular plants from the biosphere. The upper bound for the annual energy uptake is 1.62 × 10 22 J yr −1 . Today humans are consuming about 3.24 × 10 20 J annually. If humans are doubling their energy consumption every decade, and this rate is continued, then the bound would be reached and exceeded during the next 70 years. In accordance with some estimation, only 5% of the potential work of the biosphere can be used to maintain its structure (in particular, animals) and its evolution; the rest is spent to turn ‘wheels’ of the global biogeochemical cycles, then the upper bound is 1.22 × 10 20 J yr −1 . By comparing this value with the current energy uptake, 3 × 10 20 J yr −1 , we see why we already have serious problems today. Finally, the concept of ‘entropy pump’ and its application to the problem of sustainable development is discussed.