Pressure of an ideal gas. It is desired to get the pressure exerted by an ideal gas on a wall by accounting for the rate of momentum transfer from the molecules to the wall.?

(a) When a molecule traveling with a velocity v collides with a wall, its incoming velocity components are u_x, u_y, u_z, and after a specular reflection at the wall, its components are ? u_x, u_y u_z. Thus the net momentum transmitted to the wall by a molecule is 2mu_x. The molecules that have an x- component of the velocity equal to u_x, and that will collide with the wall during a small time interval ?t, must be within the volume Su_x ?t. How many molecules with velocity components in the range from u_x, u_y, u_z to u_x + ?u_x, u_y + ?u_y, u_z + ?u_z will hit an area S of the wall with a velocity u., within a time interval ?t? It will be f(u_x, u_y, u_z,)du_x, du_y?du_z: times Su_x ?t. Then the pressure exerted on the wall by the gas will be Explain carefully how this expression is constructed. Verify that this relation is dimensionally correct.?

(b) Insert Eq. 1C.1-1 for the Maxwell-Boltzmann equilibrium distribution into Eq. 1C.3-1 and perform the integration. Verify that this procedure leads to p = nkT, the ideal gas law. ??

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p= ****** (Su At) (2mu,)f(u,, u, u.)du du, du Sat