Consider a gas of N non-interacting molecules enclosed in a container of volume V0. Focus attention on any sub volume V of this container and denote by N the number of molecules located within this sub volume. Each molecule is equally likely to be located anywhere within the container; hence the probability that a given molecule is located within the subvolume V is simply equal to V/V0 a) What is the mean number ¯N of molecules located within V? Express your answer in terms of N0, V0 and V. (b) Find the relative dispersion in the number molecule located within V. Express in terms of ¯N, V and V0
¯¯¯¯
( ¯N-N/ N¯ )^2/N¯
(c) What does the answer to part (b) become when V< (d)What value should the dispersion ¯¯¯¯
( ¯N-N/ N¯ ) assume when V > V0 ? Does the answer to part (b) agree with this expectation