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The technique is closely related to using gas adsorption to measure pore sizes, but uses the Gibbs–Thomson equation rather than the Kelvin equation.They are both particular cases of the Gibbs Equations of Josiah Willard Gibbs: the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant pressure case. [1]
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is
The heat content of an ideal gas is independent of pressure (or volume), but the heat content of real gases varies with pressure, hence the need to define the state for the gas (real or ideal) and the pressure. Note that for some thermodynamic databases such as for steam, the reference temperature is 273.15 K (0 °C).
Diagram of thermodynamic surface from Maxwell's book Theory of Heat.The diagram is drawn roughly from the same angle as the upper left photo above, and shows the 3D axes e (energy, increasing downwards), ϕ (entropy, increasing to the lower right and out-of-plane), and v (volume, increasing to the upper right and into-plane).
Combining expressions for the Gibbs–Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule. One particularly useful expression arises when considering binary solutions. [7] At constant P and T it becomes:
A century later Gibbs [3] proposed a modification to Young's equation to account for the volumetric dependence of the contact angle. Gibbs postulated the existence of a line tension, which acts at the three-phase boundary and accounts for the excess energy at the confluence of the solid-liquid-gas phase interface, and is given as:
When perfectly pure, the interface between fluids usually displays only surface tension. [1] The stress within a fluid interface can be affected by the adsorption of surfactants in several ways: Change in the surface concentration of surfactants when the in-plane flow tends to alter the surface area of the interface (Gibbs' elasticity). [2]
From these meanings (which actually apply in specific conditions, e.g. constant pressure, temperature, etc.), for positive changes (e.g., ΔU > 0), we can say that ΔU is the energy added to the system, ΔF is the total work done on it, ΔG is the non-mechanical work done on it, and ΔH is the sum of non-mechanical work done on the system and ...