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Raoult's law (/ ˈ r ɑː uː l z / law) is a relation of physical chemistry, with implications in thermodynamics.Proposed by French chemist François-Marie Raoult in 1887, [1] [2] it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component (liquid or solid) multiplied by its mole fraction in the mixture.
The early identification of self-similar solutions of the second kind can be found in problems of imploding shock waves (Guderley–Landau–Stanyukovich problem), analyzed by G. Guderley (1942) and Lev Landau and K. P. Stanyukovich (1944), [3] and propagation of shock waves by a short impulse, analysed by Carl Friedrich von Weizsäcker [4] and ...
The atmospheric pressure is roughly equal to the sum of partial pressures of constituent gases – oxygen, nitrogen, argon, water vapor, carbon dioxide, etc.. In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. [1]
For example, the solution to the Dirichlet problem for the unit disk in R 2 is given by the Poisson integral formula. If f {\displaystyle f} is a continuous function on the boundary ∂ D {\displaystyle \partial D} of the open unit disk D {\displaystyle D} , then the solution to the Dirichlet problem is u ( z ) {\displaystyle u(z)} given by
The partial pressures obey Dalton's law: =, where P is the total pressure and y i is the mole fraction of the component (so the partial pressures add up to the total pressure). The fugacities commonly obey a similar law called the Lewis and Randall rule: f i = y i f i ∗ , {\displaystyle f_{i}=y_{i}f_{i}^{*},} where f *
In simple words, we can say that the partial pressure of a gas in vapour phase is directly proportional to the mole fraction of a gas in solution. An example where Henry's law is at play is the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression , going to decompression sickness .
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions. [1]