**5. Gibbs free energy, irreversibility, the atmosphere and climate heating**

Gibbs free energy – 'exergy' – is what enables, via dilution of energy density, the circulation of the atmosphere. It forces directional evolution through the most energetic high-speed molecules, giving the arrow of time to the atmosphere, and its associated irreversibility. Its 2nd Law cost is paid for by the dissipation enabled by the molecules with the most probable speeds easily exchanging energy to maintain an operationally observed temperature while enabling the evolution of vorticity and atmospheric flow, expressed as scale invariant turbulence. The basis for this is discussed in Chapter 7 of Tuck [12], arising from Alder and Wainwright [11]. The energy source is the solar beam, the dissipation is infrared dissipation to space from the infrared active molecules, mainly but not exclusively in the 7–14 μm wavelength window region, by water vapour, water vapour dimers, carbon dioxide, ozone, methane, nitrous oxide and halocarbons. These radiatively active molecules display scale invariance, ensuring that the absorption and emission of radiation operates on all scales, from the mean free path up to 15 orders of magnitude to a great circle. The long-understood fact that atmospheric state and evolution is governed by the interaction between radiation, chemistry and dynamics is extended to the smallest, microscopic scales. The transition from meso to macro scales maintains an operational temperature, and points to the reason the atmosphere 'integrates' a portion of the variability in its constituents and dynamical quantities [14].

Because the change in Gibbs free energy Δ*G* is equal to or is less than the difference between the change in enthalpy *H* and the product of the temperature *T* change and the entropy *S* change,

$$
\Delta G \le \Delta H - T\Delta S \tag{6}
$$

a thermodynamic profit in the case of amelioration of climate heating by fossil fuel burning is not possible by using power generated by those means. Consider that typical coal burning power stations operate at about 35% efficiency; 65% is dissipated. It follows that the entropy cost of any remedial intervention must be paid for by energy derived from renewable sources rather than from fossil fuel combustion. For example, the entropy cost of removing 25% of 400 ppm mole fraction of carbon dioxide from the air will be very high. **Figure 11** shows the behaviour of the Gibbs free energy derived from scaling analysis of the temperature in **Figure 1**, see [14].

#### **Figure 11.**

*The behaviour of* K*(*q*) and* K*(*q*)/*q *as a function of* q*; see Table 1 and Eqs. (1)-(5) for definitions. At* q *= 1 both functions are at or near zero, indicting a steady state condition. There is further discussion in Section 4 of [14].*

**Figure 12.**

*The relative percentages of organic and sulfate ions in the single particle laser mass spectrometry from the WB57F aircraft [24]. There is significant presence of organic molecules well into the stratosphere. See also [18, 19, 25].*

Both Gibbs free energy *K*(*q*)/*q* and the exponent in the partition function -*K*(*q*) go through zero at *q* = 1, indicating existence at or near a steady state. Input energy will move the system from steady state towards higher temperatures, with scaling Gibbs free energy enabling movement to more energetic states as *K*(*q*)/*q* becomes more negative. Cooling on the other hand will move the system to less energetic steady states at higher *q*.

The above considerations apply to geoengineering projects. Further considerations apply in the case of so-called "solar radiation management", such as the limitations of our current understanding of the chemical, radiative and cloud physical roles of aerosols in the lower stratosphere [5, 12, 18, 19]. Aerosols have been shown, over a population of millions of individual particles, to contain 45 different elements from the 92 in the periodic table, not all of course in any single particles. The aerosols are neither internally nor externally mixed at altitudes 5 to 19 km [24].

The organic content of lower stratospheric aerosols has significant effects on radiative transfer [18] and is photochemically influenced [19, 25] (see **Figure 12**).

The advantage of the statistical multifractal approach embodied in Eqs. (1)-(5) is that it can be computed for the system as a whole with adequate observations of wind speed, temperature and if necessary the radiative constituents to use Eq. (6), without having to measure all the chemical constituents of air to make what are in any case inadequate equilibrium quantum statistical thermodynamic calculations. It could also be applied to individual aerosol particles [5] via high-resolution observations and molecular dynamics calculations. These arguments, and those in the preceding sections, suggest a programme of future research.

### **6. Conclusion**

The above arguments show that the changes from fossil-fuel induced heating are irreversible in the strict sense of quantum statistical thermodynamics. This however *Scale Invariant Turbulence and Gibbs Free Energy in the Atmosphere DOI: http://dx.doi.org/10.5772/intechopen.95268*

is expected because the atmosphere is not an isolated system at equilibrium; rather it is an open system far from equilibrium. We show above that it is irreversible by statistical multifractal analysis; **Figure 11** is an example of how it works, showing that to move from an existing steady state will take energy to do work that must be enabled by the dissipation mechanism, which is infrared radiation to space. Conditions to achieve a thermodynamic profit therefore indicate that any remedial action must use renewable energy, which in principle is available in abundance given that the entire biosphere uses only about 1% or so of the incident solar beam. The many uncertainties in climate modelling; in the cloud physical, chemical, dynamical and radiative uncertainties associated with aerosols; in the inability to forecast beyond macroweather time scales all imply that geoengineering, particularly in the form of "solar radiation management", is an extremely uncertain gamble [19]. While the situation is in principle irreversible as the entropy-carrying infrared photons recede into space at the speed of light over the whole 4π solid angle, the simplest and least risky course of action is to use renewably generated Gibbs free energy to move to a sustainable steady state, by reducing and then eliminating fossil fuel burning, and to do it with despatch.
