This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PHYS 333 Winter 2009 Assignment 2 Due: 5:00 pm Friday January 16 All of these problems are from Schroeders 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 t is PA t/ (2 m v x ), where P is the pressure, m is the average molecular mass, and v x is the average xvelocity 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/ , where 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 1litre container punctured by a 1mm 2 hole....
View Full
Document
 Winter '09
 Harris
 Physics

Click to edit the document details