# 02 - Availability and Exergy Many of the analyses performed...

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Availability and Exergy Many of the analyses performed by engineers are based on the First Law of Thermo- dynamics, which is a law of energy conservation. Most mechanical engineers use the Second Law of Thermodynamics simply through its derived property - entropy (S). However, it is possible to introduce other ‘Second Law’ properties to define the maximum amounts of work achievable from certain systems. Previously, the properties Helmholtz energy (F) and Gibbs energy (G) were derived as a means of assessing the equilibrium of various systems. This section considers how the maximum amount of work available from a system, when interacting with surroundings, can be estimated. This shows, as expected, that all the energy in a system cannot be converted to work: the Second Law stated that it is impossible to construct a heat engine that does not reject energy to the surroundings. 2.1 Displacement work The work done by a system can be considered to be made up of two parts: that done against a resisting force and that done against the environment. This can be seen in Fig 2.1. The pressure inside the system, p, is resisted by a force, F, and the pressure of the environment. Hence, for System A, which is in equilibrium with the surroundings pA=F+pd (2.1) where A is the area of cross-section of the piston. Svstem A Fig. 2.1 Forces acting on a piston If the piston moves a distance dx, then the work done by the various components shown in Fig 2.1 is pA dx=F dx+pJ dx (2.2) where PA dx = p dV = SW,,, = work done by the fluid in the system, F dx = SW,, = work done against the resisting force, and pJ dx = po dV = SW,, = work done against the surroundings.

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14 Availability and exergy Hence the work done by the system is not all converted into useful work, but some of it is used to do displacement work against the surroundings, i.e. sw,,, = SW, + SW,, (2.3) which can be rearranged to give sw, = SW,,, - (2.4) 2.2 Availability It was shown above that not all the displacement work done by a system is available to do useful work. This concept will now be generalised to consider all the possible work outputs from a system that is not in thermodynamic and mechanical equilibrium with its surroundings (i.e. not at the ambient, or dead state, conditions). Consider the system introduced earlier to define Helmholtz and Gibbs energy: this is basically the method that was used to prove the Clausius inequality. Figure 2.2(a) shows the general case where the work can be either displacement or shaft work, while Fig 2.2(b) shows a specific case where the work output of System A is displacement work. It is easier to follow the derivation using the specific case, but a more general result is obtained from the arrangement shown in Fig 2.2(a). System B 6W 6WR * Reservoir To (4 .......... ,.-- '\, System B Svstem A ', 0) e7 Reservoir To Fig. 2.2 System transferring heat to a reservoir through a reversible heat engine First consider that System A is a constant volume system which transfers heat with the (2.5) Let System B be System A plus the heat engine E,.
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## This note was uploaded on 03/09/2010 for the course MECHANICAL ME9802701 taught by Professor Prof.william during the Spring '10 term at Institut Teknologi Bandung.

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02 - Availability and Exergy Many of the analyses performed...

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