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The Kelvin equation describes the change in vapour pressure due to a curved liquid–vapor interface, such as the surface of a droplet. The vapor pressure at a convex curved surface is higher than that at a flat surface. The Kelvin equation is dependent upon thermodynamic principles and does not allude to special properties of materials.
In fluid mechanics, Kelvin's circulation theorem states: [1] [2] In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869.
Capillary condensation in pores with r<10 nm is often difficult to describe using the Kelvin equation. This is because the Kelvin equation underestimates the size of the pore radius when working on the nanometer scale. To account for this underestimation, the idea of a statistical film thickness, t, has often been invoked.
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The technique is closely related to that of use of 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 ( Josiah Willard Gibbs ): the Kelvin equation is the constant temperature case, and the Gibbs–Thomson equation is the constant ...
The kelvin now only depends on the Boltzmann constant and universal constants (see 2019 SI unit dependencies diagram), allowing the kelvin to be expressed exactly as: [2] 1 kelvin = 1.380 649 × 10 −23 / (6.626 070 15 × 10 −34)(9 192 631 770) h Δν Cs / k B = 13.806 49 / 6.091 102 297 113 866 55 h Δν Cs / k B
Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have application in understanding: Generation of lift on an airfoil; Starting vortex; Horseshoe vortex; Wingtip vortices. Helmholtz's theorems are now generally proven with reference to Kelvin's circulation theorem.
The SI unit of temperature is the kelvin (K), but using the above relation the electron temperature is often expressed in terms of the energy unit electronvolt (eV). Each kelvin (1 K) corresponds to 8.617 333 262... × 10 −5 eV; this factor is the ratio of the Boltzmann constant to the elementary charge. [6]