# 01 - State of Equilibrium Most texts on thermodynamics...

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State of Equilibrium Most texts on thermodynamics restrict themselves to dealing exclusively with equilibrium thermodynamics. This book will also focus on equilibrium thermodynamics but the effects of making this assumption will be explicitly borne in mind. The majority of processes met by engineers are in thermodynamic equilibrium, but some important processes have to be considered by non-equilibrium thermodynamics. Most of the combustion processes that generate atmospheric pollution include non-equilibrium effects, and carbon monoxide (CO) and oxides of nitrogen (NO,.) are both the result of the inability of the system to reach thermodynamic equilibrium in the time available. There are four kinds of equilibrium, and these are most easily understood by reference to simple mechanical systems (see Fig 1.1). (i) Stable equilibrium w Marble in bowl. For stable equilibrium AS),* < 0 and AE)s > 0. (AS is the sum of Taylor’s series terms). Any deflection causes motion back towards equilibrium position. * Discussed later. (ii) Neutral equilibrium Marble in trough. AS), = 0 and AE)s = 0 along trough axis. Marble in equilibrium at any position in x-direction. (iii) Unstable equilibrium Marble sitting on maximum point of surface. AS)E > 0 and AE)s < 0. Any movement causes further motion from ‘equilibrium’ position. Fig. 1.1 States of equilibrium -

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2 State of equilibrium (iv) Metastable equilibrium Marble in higher of two troughs. Infinitesimal variations of position cause return to equilibrium - larger variations cause movement to lower level. Fig. 1.1 Continued *The difference between AS and dS Consider Taylor’s theorem Thus dS is the first term of the Taylor’s series only. Consider a circular bowl at the position where the tangent is horizontal. Then 1 d2S d2S However AS = dS + - - Ax2 + ... # 0, because - etc are not zero. 2 dr2 dr2 Hence the following statements can be derived for certain classes of problem stable equilibrium (ds), = 0 (As) E < 0 neutral equilibrium (dS)E = 0 (AS), = 0 unstable equilibrium (dS), = 0 (As) E > 0 (see Hatsopoulos and Keenan, 1972). 1.1 The type of equilibrium in a mechanical system can be judged by considering the variation in energy due to an infinitesimal disturbance. If the energy (potential energy) increases Equilibrium of a thermodynamic system
Equilibrium of a thermodynamic system 3 F=Tl Fig. 1.2 Heat transfer between two blocks then the system will return to its previous state, if it decreases it will not return to that state. A similar method for examining the equilibrium of thermodynamic systems is required. This will be developed from the Second Law of Thermodynamics and the definition of entropy. Consider a system comprising two identical blocks of metal at different temperatures (see Fig 1.2), but connected by a conducting medium. From experience the block at the higher temperature will transfer ‘heat’ to that at the lower temperature. If the two blocks together constitute an isolated system the energy transfers will not affect the

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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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01 - State of Equilibrium Most texts on thermodynamics...

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