Thermodynamic system, maximum work

The combination of properties U - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, namely A, the work fimction or maximum luork (because it represents the maximum work per unit mass, obtainable during any isothermal reversible change in any given system). Therefore, it is seen that... 

Other thermodynamic functions described above in that the change in free energy AG is determined solely by the initial and final states of the system. The maximum work, or maximum available energy, defined in terms of the Gibbs free energy G, which is now called the free enthalpy, is... 

The Helmholtz and Gibbs energies are useful also in that they define the maximum work and the maximum non-expansion work a system can do, respectively. The combination of the Clausius inequality 7dS > dq and the first law of thermodynamics dU = dq + dw gives... 

If the entropy of the system decreases some of the energy must escape as heat in order to produce enough entropy in the surroundings to satisfy the second law of thermodynamics. Hence the maximum work is less than IAU I. AA is the part of the change in internal energy that is free to use for work. Hence the Helmholtz energy is in some older books termed the (isothermal) work content. 

The energy relations associated with the redox processes in wastewater follow the general rules of thermodynamics (Castellan, 1975 Atkins, 1978). The Gibbs free energy, G, of the system is the major thermodynamic function defining the state — and the change in state — of the biochemical redox processes. At constant temperature and under constant pressure, AG is equal to the maximum work, which can be produced by the redox process ... 

The maximum work the system can do occurs when dP -> 0. Wi ax " P0 y When the system does the maximum work, in other words, the system undergoes a reversible process, then from the first law of thermodynamics AU = q - w = qr - wmax or qr = AU + wmax q, is the maximum amount of heat which the system can absorb from the surroundings (heat reservoir) for the vaporisation of 1 mole of water. If the pressure drop, dP, is a finite amount, i.e., dP 0, in other words, the system undergoes an irreversible process, then the system does less work for the same volume expansion w = (Po-dP)P < hw Heat transferred from the surroundings to the system is q = AU + w... 

For engineering purposes, thermodynamic calculations are useful in several respects. First, they tell us whether a proposed electrochemical system can proceed spontaneously in a given direction. Second, they tell us the maximum work that can be derived from a given cell or, conversely, the minimum work that must be expended... 

The maximum work output of any thermodynamic system or process can be obtained, if the material in the system or the working fluid in the process is brought into equilibrium with the environment reversibly. The actual work output of a technical process with combustion is much smaller because the combustion is highly irreversible. The work losses in a continuous combustion can be evaluated if the exergy (or available energy) before and after the reaction is calculated. This exergy is described by the equation ... 

In traditional fnel technology, the same fnel wonld be burned in air, producing an amonnt of heat = AH, the enthalpy of combnstion. The heat would then be nsed to rnn a heat engine-generator system to prodnce electrical power. The efficiency of conversion of heat to work is limited by the laws of thermodynamics. If the heat is supplied at temperature Th and if the lower operating temperature is T , the maximum work obtainable (see Section 13.4) is... 

We can define this position of equilibrium in another way that will be useful in our study of thermodynamics. If we allow the mass Mj to fall through a distance dh it will do work M2gdh, by lifting M2 (where Mi < MJ. If we make M2 closer in magnitude to we shall get correspondingly more work, until at Mx == M2 an infinitesimal displacement will lead to work M1 g dh. This is the maximum work Mx can do, as it is now lifting an equal mass. When Mx = M2 the system is of course at equilibrium therefore we can define the equilibrium condition of the system as that for which a small displacement leads to the system doing the maximum possible work. 

Explain clearly what is meant by a thermodynamically reversible process. Why is the reversible work done by a system the maximum work ... 

The different efficiencies of chemical lasers governed by different kinetic coupling schemes can be derived from a general statistical-thermodynamic approach to work processes in nonequilibrium molecular systems " . The two major components of this approach are the maximum entropy principle and the entropy deficiency function. The entropy deficiency is a generalized thermodynamic potential (free energy). That is, it decreases monotonically in time in spontaneous relaxation processes and provides an upper bound to the thermodynamic work performed by the system in a controlled process. For systems of weakly interacting molecules the entropy deficiency DS[X X ] is given by... 

With the exception of entropy, each of these functions reaches a minimum at equilibrium, and each decreases during spontaneous processes (at constant values of the subscripted variables). Thus each serves as a thermodynamic potential, or as a measure of the capacity for a system described by the subscripted variables to undergo some change or process. These thermodynamic potentials also provide a measure of the maximum work or heat output available from a process ... 

Thus the maximum work obtainable from real (irreversible) processes is always less than the theoretical limit given by the appropriate thermodynamic potential for ideal (reversible) processes. Alternatively, the work or heat input required to make a real process go is always more than the amount given by the thermodynamic potential for the ideal (reversible) process. Don t forget, if the > sign in the work equations looks backwards to you, the sign convention we adopted in 4.6 means that —w is the work obtainable from a system, so that w > Ax is the same as —w < —Ax, and is read —w is less than or equal to the decrease in x . ... 

Maximum work The work done in a reversible process is a definite quantity and is also the maximum obtained from the system undergoing the given change. For a reversible change, the internal pressure P is only infinitesimally different from the external pressure and hence there is always an equilibrium established. The magnitude of the work depends on the magnitude of the external pressure i.e., P dP. Maximum work, therefore is done when these two opposing pressures differ by an infinitesimally small amount i.e., when the process is thermodynamically reversible. 

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