Abstract
In this chapter, we discuss the modifications of the thermodynamical potentials of a system when it is immersed in an electrostatic field. The interaction between field and matter is described by the electric susceptibility of the material which is called dielectric constant for linear materials. The correct expressions for energy, free energy, chemical potential, and the other thermodynamic potentials due to the interaction with electrostatic fields is obtained neglecting electrostriction. The dielectric constant for dilute gases is obtained by statistical methods and, as an example, the increase of gas density following the charging of a condenser is calculated. A brief overlook to electrostriction as the second-order effect, is given in the last section.
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Notes
- 1.
This means that if we denote by h the distance between the plates and by \(\Sigma \) their area (we assume that the two dimensions are comparable) it must be \(h\ll \sqrt{\Sigma }\) thus the portion of the capacitor, in which we commit a significant error in treating the fields and the charge distribution as perfectly homogeneous, will have a very small volume compared to the volume in which our description will be accurate enough.
- 2.
Let us avoid to refer to the “pressure” of the fluid inside the condenser. In this region the fluid is not, in general, isotropic and the formalism to be used might be quite complicated.
- 3.
The density and the surface density of polarization charges is given, respectively, by \(-\mathbf {\nabla }\cdot \mathbf {P}\) and \(P_{\mathrm {n}}\).
- 4.
The denomination does not mean that the electric permittivity is a constant in the sense that it does not depend on the state variables, but means that it does not depend on the electric field.
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Saggion, A., Faraldo, R., Pierno, M. (2019). Electrostatic Field. In: Thermodynamics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26976-0_10
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DOI: https://doi.org/10.1007/978-3-030-26976-0_10
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