Appendices Appendix 1 Energy, Work, and Laws of Thermodynamics A.1 Introduction Energy (from Greek eme9qceia1—action, activity) can be generally defined as the property of a material system that characterizes the ability of this system to produce some changes in the environment (work, W). Such a work can consist of growth of the total amount of matter in a system, the uneven distribution of matter particles in space, and/or movement of these particles. Physical interactions between matter particles in a system are accompanied by the mutual transformation of different types of energy (mechanical, thermal, electromagnetic, gravitational, nuclear, and chemical). How is life ensured by energy? The laws of thermodynamics provide us with a quantitative answer to this question. Energy transductions in living self-replicating material systems (organisms) follow the laws of thermodynamics. It seems quite remarkable that the first law of thermodynamics (the law of conservation and transformation of energy) was first formulated in 1841 by the German physicist and physician Julius Robert von Mayer as the result of his studies of the energy processes in the human organism; it was only some time later that this law was applied to the systems of technical energetics. Thermodynamics deals with three types of systems: isolated, closed, and open. Hypothetical isolated (adiabatic) systems are completely self-contained, i.e., there is no exchange of matter, energy, and information with the environment. Closed systems are materially self-sufficient, but they are open energetically and informationally. In other words, there is exchange of energy and information, but not matter through the borders of closed systems. Many nonliving systems of technical energetics function in this way. Living organisms are open systems that constantly exchange matter, energy, and information with the environment. The term heat (Q) is used in thermodynamics as the measure of energy passing from one body to another. A system uses received energy to perform an external V. P. Skulachev et al., Principles of Bioenergetics, 383 DOI: 10.1007/978-3-642-33430-6, Ó Springer-Verlag Berlin Heidelberg 2013 384 Appendix 1: Energy, Work, and Laws of Thermodynamics work and also to carry out transitions between the alternative states of the components of the system. Changes in the amount of work can be calculated as the product of pressure (P) and an infinitesimal increment of volume (DV): DW ¼ PDV ðA1:1Þ Entropy (S) which is often assumed to be as a measure of disorder means the number of possible states of a thermodynamic system. That is why this parameter is a related degree of disorder in the studied system. The term entropy (from Greek entropia—turn, transformation), introduced in 1865 by the German physicist Rudolf Clausius, is now widely used in physics, chemistry, biology, and information theory. The relationship between the changes in the general amounts of heat and entropy during reversible processes follows the equation: DQ ¼ TDS ðA1:2Þ where T stands for absolute temperature. The second law of thermodynamics, formulated in 1851 by the English physicist William Thomson (Lord Kelvin), allows to predict the possibility of performance of external work. It connects entropy with directions of transfer of energy (heat) and of information across the border of a system. Reversible processes in isolated systems do not lead to growth in entropy; neither do they result in performance of useful work. Non equilibrium transformations necessary for performing work in isolated systems are inextricably linked to the approach of thermodynamic equilibrium with entropy reaching its maximal value. Once this equilibrium state is reached, no useful work can be performed in isolated systems. Entropy in closed and open systems increases when they perform external work; this can also result from their receiving information from the outside. Increase in the number of possible alternative states of a system reduces the probability of its being in the functionally operative (native) conformation; this in turn decreases the efficiency of its work. When using closed systems of technical energetics, one faces the necessity of their regular reparation. Living systems strive to minimize growth of their entropy, which might lead to an equilibrium state fatal for such systems. They maintain steady-state organization of its components at the expense of an external entropy increase. The existence of steady-state open systems, which correspond to minimal entropy production, was postulated by the Nobel Prize Laureate in Chemistry Ilya Prigogine, who in 1947 proved the fundamental theorem of thermodynamics of non equilibrium processes. It seems quite obvious that the complexity of thermodynamic descriptions of systems increases as the level of their isolation decreases. Simple equations of classical equilibrium thermodynamics cannot be directly applied to open systems, because matter flow across their borders prevents true equilibrium from being established. However, a living organism can be considered as an aggregate of interacting subsystems (organs, tissues, cells, organelles, and molecules), an assumption that makes it easier to understand the essence of energetic processes. In the majority of cases, individual reactions between the subsystem components Appendix 1: Energy, Work, and Laws of Thermodynamics 385 can be viewed as closed systems, which means that the equations of equilibrium thermodynamics can be applied to these processes. Thus, we conclude (on the basis of these equations) that for any given system the potential ability to perform work is determined by the degree of deviation of its components from the equilibrium state. To use in practice the approximate quantitative estimate of open systems, one should understand the nature of the equilibrium state of a particular chemical reaction and estimate equilibrium shift of the real reaction with respect to the equilibrium state predicted by the equations of classical equilibrium thermodynamics. It is this shift in equilibrium that determines the quantitative ability of the reaction to support performance useful work. Furthermore, the mathematical apparatus of equilibrium thermodynamics can be effectively used for the identification of ‘‘forbidden’’ reactions. Only processes leading to increase in entropy and reduction in energy reserve can proceed spontaneously (without any energy input into the system). A.2 Thermodynamic Potentials According to the second law of thermodynamics, only a portion of energy of a system can be ‘‘useful’’, i.e., can be employed to carry out a work. In 1878, the American physicist and mathematician Josiah Willard Gibbs developed the theory of ‘‘fundamental functions’’ to estimate the amount of useful energy. These functions characterized the state of a thermodynamic system depending on its main properties: number of particles (N), volume (V), pressure (P), temperature (T), entropy (S), and chemical potential of the components (l). These ‘‘fundamental functions’’ are now known as ‘‘thermodynamic potentials’’. The latter term was suggested in 1884 by the French philosopher and physicist Pierre Duhem, and it superseded the previous one due to its greater accuracy. Potential (from Greek potentia – power) corresponds to the sources, possibilities, means, and reserves that can be used to solve some problem, to reach a certain goal. Different thermodynamic potentials are optimized so as to facilitate characterization of systems with different sets of constant and variable properties (macroscopic parameters): • internal energy (U), a function of entropy (S) and volume (V); • enthalpy (H), a function of entropy (S) and pressure (P); • Helmholtz free energy (F), a function of temperature (T) and volume (V); • Gibbs free energy, also known as free enthalpy (G), a function of temperature (T) and pressure (P); • Landau potential, or grand thermodynamic potential (X), a function of temperature (T), volume (V), and chemical potential of transferred particles (l). The internal energy of a system (U) is defined as the total energy of the given system minus the kinetic energy of the system as a whole (energy of motion in the environment) and the potential energy of the system in external force fields (when 386 Appendix 1: Energy, Work, and Laws of Thermodynamics relating to other systems). When applied to bioenergetics, internal energy can be defined as the sum of kinetic energy of chaotic motion, potential energy of interaction, and intramolecular energy of its molecules. According to the first law of thermodynamics, the total energy of a system is equal to the difference between the amount of heat (Q) transferred to the system and the performed external work (W): U ¼ Q À W ðA1:3Þ For idealized processes comprising consecutive equilibrium states, changes of internal energy of a system with a constant number of particles during performance of work (DU) are described by the equation: DU ¼ DQ À DW ¼ TDS À PDV ðA1:4Þ Thermodynamic potential H, or enthalpy (from Greek enthálpo¯—heating), is used to characterize the amount of heat transferred to a system for the performance of work. Changes in enthalpy are connected to the internal energy of a system as follow: DH ¼ DU þ DðÞ¼PV TDS À PDV þ PDV þ VDP ¼ TDS þ VDP ðA1:5Þ For constant pressure, enthalpy change is equal to the amount of heat transferred to the system for the performance of useful work; that is why enthalpy is often referred to as heat function, or heat content. It is convenient to use enthalpy