Examples of State Functions in Thermodynamics

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State functions in thermodynamics are properties that depend solely on the current state of a system, not on the path taken to reach that state. Key examples include internal energy, enthalpy, and entropy, which are extensive properties, as well as intensive properties like temperature, pressure, density, and viscosity. These functions provide crucial insights into the thermodynamic behavior of systems. Understanding these state functions is essential for analyzing energy exchanges and transformations in thermodynamic processes. The discussion highlights the importance of distinguishing between extensive and intensive state functions in thermodynamics.
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I'm curious to find more examples (if they exist) of state functions in thermodynamics other than the internal energy of a gas.

Is the pressure, volume and temperature of a gas all state functions of the system?
 
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State function of a system is in thermodynamics any function that does not depend on the processes undergone by the system but only on the present state. In addition to internal energy are state functions enthalpy H, entropy S, isochoric-isothermic potential F, isobaric-isothermic potential \Phi, all of them extensive (mass-dependent, additive) functions; temperature, density, viscosity etc. (I guess also pressure) in a thermodynamic system are intensive (non-additive) state functions.
(quoted from B.Javorskij, A.Detlaf "Manuale di fisica", translated by myself from Italian)
 
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Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
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