Limits to energy conversions

Energy conversions play a central role in driving the dynamics of Earth system processes. In the last chapter, we have seen how energy conversions are governed by the first and second law of thermodynamics. Energy conversions and the associated dissipative processes are sustained in natural systems by the entropy exchange across the system's boundary and are constrained by the second law. The subsequent generation of free energy out of this entropy exchange maintains the disequilibrium associated with a variety of variables and is reflected in the dynamics of the Earth system.

In this chapter, we take the laws of thermodynamics a step further.We first show how these laws yield fundamental conversion limits when combined, which then set the dissipative “speed limits” for the dynamics of a system. It sets the limit on the rate by which work can be performed through time, that is, the power that is associated with the conversion of thermal energy into another form. When applied to the Earth system, it is important to note that the work is performed inside the system, so that the consequences of the work need to be taken into account in the formulation of thermodynamic limits.

To illustrate thermodynamic limits qualitatively, consider the energy conversion associated with the heat engine shown in Fig. 4.1a. A heat engine is an abstract device that converts thermal energy into mechanical work and can represent a steam engine, a turbine, or atmospheric convection. The heat engine is driven by a heat flux Jin, from a hot reservoir, expels a certain fraction into a so-called waste-heat flux Jout, to a cold reservoir, and converts the other fraction into work at a rate G, with work performed through time representing the power of the engine. The heat flux Jout is referred to as a waste heat flux because its energy is not converted into free energy. The entropy exchange of the heat engine only consists of the heat fluxes between the reservoirs with their respective temperatures. This entropy exchange decreases the greater the value of G, because for the same entropy import associated with Jin, less is exported by Jout. The second law sets the ultimate limit to G, because the heat engine needs to at least export as much entropy as it is imported to maintain a non-negative entropy exchange.