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Liquid oxygen has a clear cyan color and is strongly paramagnetic: it can be suspended between the poles of a powerful horseshoe magnet. [2] Liquid oxygen has a density of 1.141 kg/L (1.141 g/ml), slightly denser than liquid water, and is cryogenic with a freezing point of 54.36 K (−218.79 °C; −361.82 °F) and a boiling point of 90.19 K (−182.96 °C; −297.33 °F) at 1 bar (14.5 psi).
The function f(x) = √ x defined on [0, 1] is not Lipschitz continuous. This function becomes infinitely steep as x approaches 0 since its derivative becomes infinite. However, it is uniformly continuous, [8] and both Hölder continuous of class C 0, α for α ≤ 1/2 and also absolutely continuous on [0, 1] (both of which imply the former).
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
According to the continuity equation, the negative divergence of this flux equals the rate of change of the probability density. The continuity equation reflects the fact that the molecule is always somewhere—the integral of its probability distribution is always equal to 1—and that it moves by a continuous motion (no teleporting).
In a liquid mixture, the fugacity of each component is equal to that of a vapor component in equilibrium with the liquid. In an ideal solution, the fugacities obey the Lewis-Randall rule: =, where x i is the mole fraction in the liquid and f ∗ i is the fugacity of the pure liquid phase. This is a good approximation when the component ...
By 1877 sprays of both liquid oxygen and liquid nitrogen had been produced, and a new field of research, low temperature physics, had been opened. The van der Waals equation played a part in all this, especially with respect to the liquefaction of hydrogen and helium which was finally achieved in 1908. [37]
A function f with variable x is continuous at the real number c, if the limit of (), as x tends to c, is equal to (). There are several different definitions of the (global) continuity of a function, which depend on the nature of its domain .
Then f (−1) = f (1), but there is no c between −1 and 1 for which the f ′(c) is zero. This is because that function, although continuous, is not differentiable at x = 0. The derivative of f changes its sign at x = 0, but without attaining the value 0.