Maxwell distribution function

MSN.2. I. Prigogine and E. Xhrouet, On the perturbation of Maxwell distribution function by chemical reactons in gases, Physica 15, 913-932 (1949). 

This is the well-known Maxwell distribution function. If we now evaluate the thermodynamic potential (10) at the equilibrium states (12) we obtain... 

Equivalently, M w = n r, v)eMi X = 0, where X is the thermodynamic force given in (79). The elements of M w are the local Maxwell distribution functions. They are denoted hereafter by the symbol... 

Specific Surface. A first possibility is to assume a certain shape of the pores and carry out a summation over all pores. If one for instance assumes that the pores are ellipsoids and chooses a Maxwell distribution function then one obtains for prolate ellipsoids (Figure 5) ... 

The mean turbulent velocity of eddies with size A in the inertial subrange of isotropic turbulence was assumed equal to the velocity of the neutrally buoyant droplets measured by Kuboi et al [53, 54]. Kuboi et al [53, 54] found that the turbulent velocity of droplets could be expressed by the Maxwell distribution function (9.32), thus the mean eddy velocity was approximated by ... 

The molecular velocities are distributed according to the Maxwell distribution function... 

The equation (12) is Maxwell distribution function for a gas and describes the ecjuilihrium state of distribution function f. The constants can find if replace equation (12) whit conservation laws obtains the common form of Maxwell s distribution function... 

In an ideal gas, the distribution of molecular speeds is given by the Maxwell distribution function. 

To calculate the collision density an estimate of the length of the relative velocity between a pair of unlike particles, taking into account the distribution of particle velocities, is required. From kinetic theory of gases, we know that Urei,i,2 = (vj + Uj) can be justified by a detailed calculation with the Maxwell distribution function (See Present [101], p. 53 and p. 79). However, this relation is not generally valid for bubble, drops and particles. The approximation ... 

In most real cases, the function f(v) is the Maxwell distribution function, which is related to the fast establishment of the equilibrium distribution over velocities due to elastic processes. The Maxwell distribution function over relative velocities has the form... 

The rate constant and cross section are related between each other duough the distribution functiony(v, T) by expression (2.18). Using this expression with the Maxwell distribution function d[v, T), we can write expressions for the rate constants of the forward k(jj — l,m) and reverse /,m — iJ) reactions. 

The fission neutrons from a fuel assembly surrounded by a moderator are slowed down by a number of elastic scattering collisions with the moderator atoms. The final average kinetic energy of the neutrons is approximately the same as that of the atoms (or molecules) of the moderator. Since the number of moderator atoms having speeds within a certain range is described by the Maxwell distribution function of molecular speeds, this same function may be used to describe the neutrons that are in thermal equilibrium with the moderator atoms (that is, thermal neutrons) ... 

Solution The number of molecules whose speeds he in a narrow interval u-u+du can be determined according to an approximate equation dA + =iV/(i))du where N is the total number of molecules in the given volume, f(o) is the Maxwell distribution function (3.3.6). In order to determine the amount of molecules sought, we have to substitute the distribution function into the expression and calculate a corresponding integral. Therefore,... 

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