Energy equationKinetic energyPotential energyThe paper introduces the energy equation in a multi-dimensional spacetime. Firstly, we use a new relation between kinetic energy and potential energy. Secondly, we obtain total energy based on potential energy and kinetic energy. Thirdly, we present the ...
A second-order differential equation is derived for the electric potential of an electron system with slowly varying density. It includes consistently the first-gradient corrections to both the kinetic energy and the exchange energy. In the regime of high density, the equation reduces to the one ...
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As was defined mathematically, this property can be used to measure the change of Gibbs free energy, G, in the system with the change in the amount of substance i as a constant: pressure, p; temperature, T; and amount of other components, nj, where ni is the amount of component i ...
When there is no change in chemical conditions, kinetic energy and potential energy, these terms can be neglected in the balance equation. As mentioned earlier, the exergy of work transfer (ExW) is identical to the energy in work ExW = W. Nevertheless, when the system imposes against a movi...
For this purpose we will use similar approach that Dirac23 has used to linearise the relativistic energy. The idea of the linearization of the Lagrangian in HJB equation is the main idea in this paper and we will see that this idea will lead us to the derivation of Dirac equation. We ...
Electric Potential Equation For any point charge Q, there always exists an electric field in the space surrounding it. If another charge q is brought from infinity (far away) and placed in the electric field of the charge Q, then the electric potential energy (E.P.E.) for the system of...
We consider the Dirichlet problem for the energy-critical heat equationut=Δu+u5inΩ×R+,u=0onΩ×R+,u(x,0)=u0(x)inΩ,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{...
where θ is the total energy of a flowing matter, which represents the sum of internal energy, flow work, kinetic energy, and potential energy defined by (143)θ=u+Pv+12u2+gz=h+12u2+gz In a steady flow system, mass flow rate, pressure, temperature, etc. do not change in time, the...
(same dielectric constant1) and has properties like the bulk solution; the electrical potential is a maximum at the charged surface and drops to zero in the bulk solution; the change in ion concentration from the charged surface to the bulk solution is nonlinear; and only electrostatic ...