Abstract
Herein we study the classical thermodynamics of multicomponent elastic solids as open systems. By writing down explicit expressions for the heat form and the work form, a simple derivation of the fundamental thermodynamic equations for elastic solids as open systems is presented. In particular a formula is obtained for the heats of mass transfer of the chemical components. This paper ends with a rebuttal to the contention that heat can not be unambiguously defined for open, classical reversible systems.
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Notes
This “neoclassical” designation is mine. Serrin never used the term “neoclassical thermodynamics”.
The term \(\boldsymbol{\sigma }\cdot d(V_{R} \boldsymbol{E})\) for mechanical work can appear in many equivalent versions where \(\boldsymbol{\sigma}\) and \(\boldsymbol{E}\) are replaced by other conjugate pairs of stress and strain. See, e.g., McLellan [8] for examples.
This assumption is indirectly justified when we show in Sect. 5 that the Second Law implies \(TdS = q\). Contrary to the position taken here, some hold the opposite view. For instance, Münster [7, p. 46] asserted that “[i]t is …not generally possible to define clearly the ‘volume work’ on an open phase. This removes, at the same time, the basis for the definition …of the heat absorbed.” The concept of work for open systems warrants a direct and more detailed general discussion, which goes beyond the scope of the present note.
Here, for easy comparison with formulas in the physics and chemistry literature, we use the same symbol \(\mu_{i}\) to denote \((\partial G/\partial N_{i})_{T, \boldsymbol{\sigma}, \hat{N}_{i}}\). Since \(M_{i} = m_{i} N_{i}\), where \(m_{i}\) is the molecular weight of the \(i\)-th chemical component, the chemical potential as defined in (35) is equal to \(m_{i}\) times the \(\mu _{i}\) that appears in (32).
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Man, CS. Classical Thermodynamics of Elastic Solids as Open Systems. J Elast 126, 271–280 (2017). https://doi.org/10.1007/s10659-016-9591-4
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DOI: https://doi.org/10.1007/s10659-016-9591-4