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The thermodynamics of fluid systems. Paperback ed. (English) Zbl 0581.76001
The Oxford Engineering Science Series, 2. Oxford: Clarendon Press. XI, 359 p. £12.50 (1985).
This is the paperback edition of the well known text book first published in 1975 suitable for postgraduate students in physics, mathematics and basic engineering sciences. Starting out with the concept the choice of state space depends on used time-scale the approach wants to make clear the unity of classical, kinetic, statistical, and non-equilibrium thermodynamics. There are two parts: equilibrium and process thermodynamics. Part one ranges from classical thermodynamics including systems with internal variables to statistical thermodynamics. Part two contains an approach to Onsager-Casimir reciprocal relations of coupled irreversible processes which will be discussed below. Other topics of this part are frame indifference and material invariance, fluid mixtures including Helium II, magnetoplasmas, internal coordinates, linear response theory, the fluctuation-dissipation theorem, and kinetic processes. Remarks on rational thermodynamics are missing. The 1975 first edition was celebrated by H. A. Buchdahl: ”This book is superb”. Ten years later one can say: This book is still scarcely superb because there are some shortcomings.
The first law is introduced in Born’s formulation using adiabatically enclosed systems but nothing is said about that internal energy is only definable for states which are adiabatically accessible. Therefore a common gauge of internal energy of different classes of adiabatically accessible states is necessary and possible. The second law is formulated as work criterion: Adiabatic work must be strictly positive for processes being cyclic in the work variables. The existence of entropy following from this formulation of the second law is demonstrated elegantly. But the connexion of Clausius’ inequality with the second law is missing, moreover the proof of Clausius inequality is awful, because it has nothing to do with stability conditions.
In sec. 23.2 a definition for temperature of non-equilibrium states is given which has nothing to do with a measuring quantity. Because modern concepts as ”accompanying processes” are missing in the textbook this ”non-equilibrium” temperature cannot be identified as a thermostatic temperature of an accompanying process.
The idea that depending on time scale in different state spaces there are different defined entropies is clearly worked out. Equilibrium statistical thermodynamics is introduced by the usual two axioms on equal probability and maximality.
The process thermodynamics is starting by introducing a state space using relaxation variables as the only non-equilibrium ones. This procedure is adequate for treating discrete systems although no sharp distinction is made between discrete systems and field formulation. According to the preface a new (phenomenological) approach of the reciprocal relations is offered. This approach as so many forerunners is not conclusive because the odd parity of entropy production to microscopic reversibility is simultaneously used with its even parity in the so called irreversibility condition. But a non-vanishing entropy production cannot have odd and even parity simultaneously.
Disregarding axiomatic strictness and other topics for which more stringency is desirable the textbook attracts by its wide range of items. It is valued as a first broad reviewing introduction to thermodynamics in connexion with further reading.
Reviewer: W.Muschik

##### MSC:
 76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics 80-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics 82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics 82B35 Irreversible thermodynamics, including Onsager-Machlup theory 76Y05 Quantum hydrodynamics and relativistic hydrodynamics