Chapter 7

Consider a two-dimensional gas constrained to the $x-y$ plane so that the velocity distribution function becomes $$f(\mathit{V})=\left(\frac{m}{2\pi kT}\right)\exp [-\frac{m(V_x^2+V_y^2)}{2kT}].$$ where $m$ is the particle mass. a. Determine the corresponding speed distribution function, $f(V)$. b. Verify that the total flux of particles at the walls of a two-dimensional enclosure is given by $J=n(\mathrm{V}⟩/\pi$, where $n$ is the particle surface density (molecules $/{\mathrm{cm}}^2$ ). c. Evaluate the particle flux, $J$, for the speed distribution function of part (a). d. Demonstrate that the pressure for a two-dimensional gas is $P=nkT$. Why would you expect this result?