Formulas kinetic energy

E is e ElRT. This is a very small fraction when E is several times greater than RT. For some fixed value of E the fraction increases very quickly with increase in T. Let us consider as an example what proportion of the molecules of a gas at 1,000° absolute possess, according to this formula, kinetic energies of translation corresponding to 20,000 calories per gram molecule. The fraction is 20000... 

Particulate Section 2.4 Chemical formula Kinetic energy... 

For small p the contribution of paths with large x (n 0) to the partition function Z is suppressed because they are associated with large kinetic-energy terms proportional to v . That is why the partition function actually becomes the integral over the zeroth Fourier component Xq. It is therefore plausible to conjecture that the quantum corrections to the classical TST formula (3.49a) may be incorporated by replacing Z by... 

The subscript S denotes tiiat it is the kinetic energy calculated from a Slater determinant. The A = 1 case corresponds to interacting electrons, and eq. (6.4) is therefore only an approximation to the real kinetic energy, but a substantial improvement over the TF formula (eq. (6.2)). 

Kinetic energy equals 1/2 mass x speed/ Therefore, a formula for the change of the square of the speed is... 

Kelvin temperature scale, 58 Ketones, 334 Kerosene. 231, 341 Kilo, 40 Kilocalorie, 40 Kinetic energy, 53, 114 billiard ball analogy, 6, 114 distribution, 130, 131 formula for, 59 of a moving particle, 59 relation to temperature, 56, 131 Kinetic theory, 49, 52, 53 and Avogadro s Hypothesis, 58 review, 61... 

Wigner s formula is open to criticism also on another point, since he assumes the existence of a stationary electron state where the density is so low that the kinetic energy may be neglected. This is in contradiction to the virial theorem (Eq. 11.15), which tells us that the kinetic energy can never be neglected in comparison to the potential energy and that the latter quantity is compensated by the former to fifty per cent. A reexamination of the low density case would hence definitely be a problem of essential interest. 

This meter may thus be considered as an orifice meter with a variable aperture, and the formulae already derived are therefore applicable with only minor changes. Both in the orifice-type meter and in the rotameter the pressure drop arises from the conversion of pressure energy to kinetic energy and from frictional losses which are accounted for in the coefficient of discharge. The pressure difference over the float —AP. is given by ... 

In any circumstances, it can be expected that and (5x are algebraic functions of turbulence length scale and kinetic energy, as well as chemical and molecular quantities of the mixture. Of course, it is expedient to determine these in terms of relevant dimensionless quantities. The simplest possible formula, in the case of very fast chemistry, i.e., large Damkohler number Da = (Sl li)/ SiU ) and large Reynolds Re = ( Ij)/ (<5l Sl) and Peclet numbers, i.e., small Karlovitz number Ka = sjRej/Da will be Sj/Sl =f(u / Sl), but other ratios are also quite likely to play a role in the general case. 

Does it bother you to find that neither the chemical formula nor the molar mass is needed for these calculations Remember that not all data are necessarily required for any particular calculation. Because average kinetic energy depends on temperature but not on molar mass, we do not need mass information to do this problem. 

The various terms in this formula have the meaning of the potential function (force field) V(r1,r2,0) the vibrational, 7 rotational, fx, Ty, Tz and rotational-vibrational, Tvr kinetic energy terms. The latter are differential operators acting in the space of wave functions )/(/ ,r2,0 a,P,y). The potential function V(rur2,Q) is either calculated ab initio or parametrized in a suitable fashion. A commonly used parametrization is that provided by the force-field method... 

The classical kinetic energy T is given by the usual formula involving the time derivatives (velocities) of the Cartesian coordinates x ,... 

Decius JC (1948) A tabulation of general formulas for inverse kinetic energy matrix elements in acyclic molecules. J Chem Phys 16 1025-1034... 

The effective hamiltonian in formula 29 incorporates approximations that we here consider. Apart from a term V"(R) that originates in nonadiabatic effects [67] beyond those taken into account through the rotational and vibrational g factors, other contributions arise that become amalgamated into that term. Replacement of nuclear masses by atomic masses within factors in terms for kinetic energy for motion both along and perpendicular to the internuclear axis yields a term of this form for the atomic reduced mass. 

This follows directly from the definition of the kinetic energy and the formula at Eq. (99). Note that the first term in the above formula is the von Weiszacker kinetic energy Tyf[jp which for a two-electron system is equal to the Kohn-Sham kinetic energy The term with Vtm therefore contributes to the... 

This formula for the kinetic energy corresponds to assuming that the 2-matrix has the form... 

Temperature and pressure are calculated from standard formulas from statistical mechanics (equipartition kinetic energy and virial, respectively), and are regulated at preset values by computational thermostats and barostats. 

The dotted lines in Fig. 1 show the stopping powers for the different ions at a constant velocity in units of MeV/amu. This unit of energy is very often used in heavy ion radiolysis and it is based on the classical formula for kinetic energy, E = V2 MV, where M is the heavy ion mass. As seen in Eq. (1), the ion velocity is a dominant parameter in energy loss processes and the MeV/amu energy unit is more convenient to use than converting to absolute velocity units. Remember that MeV/amu is actually proportional to the square of the velocity. 

Since each internal vibration contributes two square terms, kinetic energy and potential energy, 4 to 6 internal vibrations must be involved in the activation of the ethers, and about 12 in the activation of azomethane. For most of the molecules, the formulae of which are given in the above table, therefore, the result is very plausible. 

To a first approximation, one can assume that the kinetic energies of the fission fragments are the result of the Coulomb repulsion of the fragments after scission. A handy pocket formula that gives the total kinetic energy is... 

---