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Unformatted text preview: PHYS 333 Winter 2009 Assignment 2 Due: 5:00 pm Friday January 16 All of these problems are from Schroeder’s book. 1. Schroeder, problem 1.22 If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a rough estimate of the rate at which gas escapes through a hole. (This process is called effusion , at least when the hole is sufficiently small.) (a) Consider a small portion (area = A) of the inside wall of a container full of gas. Show that the number of molecules colliding with this surface in a time interval Δ t is PA Δ t/ (2 m ¯ v x ), where P is the pressure, m is the average molecular mass, and ¯ v x is the average x-velocity of those molecules that collide with the wall. (b) If we now take away this small part of the wall of the container, the molecules that would have collided with it will instead escape through the hole. Assuming that nothing enters through the hole, show that the number N of molecules inside the container as a function of time is governed by the differential equation dN dt =- A 2 V s k B T m N Use the approximation that ¯ v x ' ( ¯ v 2 x ) 1 / 2 = p k B T/m . Solve this equation (assuming constant temperature) to obtain a formula of the form N = N (0) e- t/τ , where τ is a “characteristic time” for N (and P ) to drop by a factor e . (c) Calculate the characteristic time for air at room temperature to escape from a 1-litre container punctured by a 1-mm 2 hole....
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This note was uploaded on 04/11/2010 for the course PHYS 333 taught by Professor Harris during the Winter '09 term at McGill.
- Winter '09