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Unformatted text preview: Chem 120B Problem Set 1 Due: February 1, 2008 1. (i) Problem 16-6 in McQuarrie & Simons Physical Chemistry textbook. (ii) Let N be the number of molecules contained in the ultra-high vacuum chamber of Problem 16-6. How large are typical fluctuations in N ? Using results from lecture, calculate both their absolute size, radicalbig ( ( N ) 2 ) , as well as their size relative to the mean, radicalbig ( ( N ) 2 ) / ( N ) . (iii) Assume that the distribution of N is Gaussian, P ( N ) e ( N ( N ) ) 2 / 2 ( ( N ) 2 ) . Estimate the likelihood of a 10% fluctuation in density by computing p (0 . 9 ( N ) ) /p ( ( N ) ) for the apparatus described in Problem 16-6. 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, ( ( A ) 2 ) = ( A 2 ) ( A ) 2 . (Here, as usual, the fluctuation in A is defined as A = 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....
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