Question 04/05

LINEAR MOLECULES

Consider a two-dimensional gas of molecules inside a rectangular box of small width d and very large length. If the box is filled by point-like molecules with density n, then the pressure is p=nk_BT. (k_B is the Boltzmann constant, and T is the temperature.) If the point-like molecules are replaced by thin linear molecules of length L, then the pressure will slightly increase.
(a) Consider a case when L is smaller (but not much smaller) than d, and the molecules do not interact with each other, but they cannot penetrate the walls of the box. (See picture (a).) Calculate the exact pressure in the box.
(b) Consider a case when the molecules of lengths L form rigid circles of diameter L/{pi}. (See picture (b).) Calculate the exact pressure in the box.
(c) Note that your answers to (a) and (b) produced corrections to the leading term (nk_BT) that are simply related to each other. What is the reason for that simple relation?

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