Closed system maximum work

The pressure increase depends on the nature of the pressure source, that is, gas or vapor pressure. Further, the characteristics of the system, that is, if the reactor is closed or open to the atmosphere will determine the consequences. In an open system, the gas or vapor will be released from the reactor, whereas in a closed system, the result of a runaway will be a pressure increase. The resulting pressure can be compared to the set pressure of the pressure relief system (Pset) or to the maximum allowed working pressure (PJ, or also to the test pressure (PM) of the equipment... 

The relation expressed in Equation (12.31) is consistent with the relation between a change of the Gibbs energy and the maximum work (excluding pressure-volume work) that a system may do on the surroundings. A galvanic cell may be considered as a closed system operating at constant temperature and pressure. Then, from Equations (7.7) and (12.31),... 

Helmholtz energy (sometimes also called Helmholtz free energy, or Helmholtz function) is the thermodynamic state function equal to the maximum possible nonexpansion work output, which can be done by a closed system in an isothermal isochoric process (T = const, V = const). In terms of the -> internal energy and -> entropy... 

When AG is negative, the maximum work that can be done by the spontaneous process within a closed system at constant T and P is given by — AG. When AG is positive, the process is not spontaneous, and AG is then the minimum work that must be provided to the system to drive the process. While the reaction pathway followed has no effect on the free energy change of the reaction, the pathway does determine the amount of useful work than can be obtained from a spontaneous reaction process. The free energy change, AG, is a measure of the work that could theoretically be obtained from a reaction, but this amount of work could only be realized if the reaction or process were conducted in a reversible manner, that is, at nearequilibrium conditions where there is a very small driving force. 

The entropy concept allows us to define two new extensive thermodynamic variables the Helmholtz Free Energy, F, which is the maximum amount of work a system can do at constant temperature (isothermal changes) and the Gibbs Free Energy, G, which is the maximum amount of work a system can do at constant pressure (isobaric changes) and is a minimum for closed systems at equilibrium with a fixed temperature and pressure. 

The changes of A and G in closed systems correspond to the maximum work performed by or on the system. cL4 is identical to the work carried out during an isothermal reversible change. dG is identical to the non-expansion work carried out under isothermal, isobaric, reversible conditions. In other words -dG corresponds to the maximum non-expansion work (e.g. electrical work) that can be generated by a closed system at constant p and T. 

As described in Sections 1.6.1 and 1.7.1 the maximum electrical work done on or by a closed system of constant composition is given by... 

The functions A and G are called potentials because allow the calculation of the maximum work only from Initial and final states. Consider a reversible process in a closed system. The maximum work can be produced only by a reversible transformation. Eqs (5.15) and (5.26), can be combined to give the following relation ... 

High-pressure operations should be carried out only with equipment specifically built for this use and only by those trained especially to use this equipment. Reactions should neva- be carried out in, nor heat applied to, an apparatus that is a closed system unless it has been designed and tested to withstand pressure. To ensure that the equipment has been properly designed, each pressure vessel should have stamped on it, or on an attached plate, its maximum allowable working pressure, the allowable temperature at this pressure, and the material of construction. Similarly, the relief pressure and setting data should be stamped on a metal tag attached to installed pressure-relief devices, and the setting mechanisms should be sealed. Relief devices used on pressure regulators do not require these seals or numbers. 

We now seek criteria for the maximum work that can be done on the surroundings by a closed system. For a system at constant temperature, Eq. (4.1-5) is... 

The term exergy will be used here and it will be extended to include all the maximum obtainable work associated with different forms of energy (thermal, electrical, etc.). For other related terms that are used in the literature, see Kenney (p.22). For the case of a closed system, see Problem 5.57. 

Combustion. The primary reaction carried out in the gas turbine combustion chamber is oxidation of a fuel to release its heat content at constant pressure. Atomized fuel mixed with enough air to form a close-to-stoichiometric mixture is continuously fed into a primary zone. There its heat of formation is released at flame temperatures deterruined by the pressure. The heat content of the fuel is therefore a primary measure of the attainable efficiency of the overall system in terms of fuel consumed per unit of work output. Table 6 fists the net heat content of a number of typical gas turbine fuels. Net rather than gross heat content is a more significant measure because heat of vaporization of the water formed in combustion cannot be recovered in aircraft exhaust. The most desirable gas turbine fuels for use in aircraft, after hydrogen, are hydrocarbons. Fuels that are liquid at normal atmospheric pressure and temperature are the most practical and widely used aircraft fuels kerosene, with a distillation range from 150 to 300 °C, is the best compromise to combine maximum mass —heat content with other desirable properties. For ground turbines, a wide variety of gaseous and heavy fuels are acceptable. 

---