Effusion: A box contains a perfect gas at temperature T and density n.
(a) What is the one-particle density, ?1(~v), for particles with velocity ~v?A small hole is opened in the wall of the box for a short time to allow some particles to escape into a previously empty container.
(b) During the time that the hole is open what is the flux (number of particles per unit time and per unit area) of particles into the container? (Ignore the possibility of any particles returning to the box.)
(c) Show that the average kinetic energy of escaping particles is 2kBT. (Hint: calculate contributions to kinetic energy of velocity components parallel and perpendicular to the wall separately.)(d) The hole is closed and the container (now thermally insulated) is allowed to reachequilibrium. What is the final temperature of the gas in the container?
(e) A vessel partially filled with mercury (atomic weight 201), and closed except for a hole of area 0.1mm2 above the liquid level, is kept at 00C in a continuously evacuated enclosure.After 30 days it is found that 24mg of mercury has been lost. What is the vapor pressure of mercury at 0^0C?