This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chem 120B Problem Set 1 Due: February 1, 2008 1. (i) Problem 166 in McQuarrie & Simon’s Physical Chemistry textbook. (ii) Let N be the number of molecules contained in the ultrahigh vacuum chamber of Problem 166. How large are typical fluctuations in N ? Using results from lecture, calculate both their absolute size, radicalbig ( ( δN ) 2 ) , as well as their size relative to the mean, radicalbig ( ( δN ) 2 ) / ( N ) . (iii) Assume that the distribution of N is Gaussian, P ( N ) ∝ e − ( N −( N ) ) 2 / 2 ( ( δN ) 2 ) . Estimate the likelihood of a 10% fluctuation in density by computing p (0 . 9 ( N ) ) /p ( ( N ) ) for the apparatus described in Problem 166. Would such a relative fluctuation be more or less likely at higher pressures? 2. (i) Show that the mean square fluctuation in any quantity A can be written in terms of its mean and mean square values, ( ( δA ) 2 ) = ( A 2 ) − ( A ) 2 . (Here, as usual, the fluctuation in A is defined as δA = A − ( A ) .) (ii) Generalize this result to the case of two different fluctuation quantities, i.e., show that(ii) Generalize this result to the case of two different fluctuation quantities, i....
View
Full
Document
This note was uploaded on 04/02/2008 for the course CHEM 120B taught by Professor Geissler during the Spring '08 term at Berkeley.
 Spring '08
 Geissler
 Physical chemistry, Mole, pH

Click to edit the document details