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In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [1] [2] [3] Albert Einstein in 1905, [4] and by Marian Smoluchowski in 1906 [5] in their works on Brownian motion.
The Einstein field equations (EFE) may be written in the form: [5] [1] + = EFE on the wall of the Rijksmuseum Boerhaave in Leiden, Netherlands. where is the Einstein tensor, is the metric tensor, is the stress–energy tensor, is the cosmological constant and is the Einstein gravitational constant.
The ideal gas law is the equation of state for an ideal gas, given by: = where P is the pressure; V is the volume; n is the amount of substance of the gas (in moles) T is the absolute temperature; R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The mathematical similarities between the expressions for shear viscocity, thermal conductivity and diffusion coefficient of the ideal (dilute) gas is not a coincidence; It is a direct result of the Onsager reciprocal relations (i.e. the detailed balance of the reversible dynamics of the particles), when applied to the convection (matter flow ...
where P is the pressure, V is the volume, N is the number of gas molecules, k B is the Boltzmann constant (1.381×10 −23 J·K −1 in SI units) and T is the absolute temperature. These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for ...
Einstein discussed his idea with mathematician Marcel Grossmann and they concluded that general relativity could be formulated in the context of Riemannian geometry which had been developed in the 1800s. [10] In 1915, he devised the Einstein field equations which relate the curvature of spacetime with the mass, energy, and any momentum within it.
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.