Using the Maxwell distribution function, calculate the mean velocity projection `(v_x)` and the mean value of the modules of this projection `lt lt |v_x| gt gt` if the mass of each molecule is equal to `m` and the gas temperature is `T`.

From the Maxwell distribution function frind lt lt v_x^2 gt gt , the mean value of the squared v_x projection of the molecular velocity in a gas at a temperature T . The mass of each molecule is equal to m .

Making use of the Maxwell distribution function, find lt lt 1//v gt gt , the mean value of the reciprocal of the velocity of molecules in an ideal at a temperature T , it the mass of eacd molecule is equal to m . Compare the value obtained with the reciprocal of the mean velocity.

Making use of the Maxwell distribution function, calculate the number v of gas molecules reaching a unit area of a wall per unit time, if the concentration of molecules is equal to n , the temperature to T , and the mass of each molecule is m .

Using the Maxwell distribution function, determine the pressure exterted by gas on a wall, if the gas temperature is T and the concentration of molecules is n .

Find the fraction of molecules whose velocity projections on the x axis fall within the inerval from v_x to v_x + dv_x , while the moduli of perpendicular velocity components fall within the inerval from v_( _|_) to v_(_|_) + dv_(_|_) . The mass of each molecule is m , and the temperature is T .

In the case of gaseous nitrogen find : (a) the temperature at which the velocities of the molecules v_1 = 300 m//s and v_2 = 600 m//s are associated with equal values of the Maxwell distribution friction F (v) , (b) the velocity of the molecules v at which the value of the Maxwell distribution function F (v) for the temperature T_0 will be the same as that for the temperature eta times higher.

For the following distribution function F(x) of a r.v. X P(3 lt X le 5)=

At what temperature of a gas will the number of molecules, whose velocities fall within the given interval from v to v + dv , be the greatest ? The mass of each molecule is equal to m .

For the following distribution function F (X) of a r.v. X P(3 lt X le 5)=

At the moment t=0 a point starts oscillating along the x axis according to the lasw x=a sin omegat t . Find: (a) the mean value of its velocity vector projection ( : v_(x) : ) , (b) the modulus of the mean velocity vector |( : v : )| , (c) the mean value of the velocity modulus ( : v : ) averaged over 3//8 of the period after the start.