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hwk3 - Ω E ∝ V N E 3 N 2(1 Consider a container of...

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PH421 - Thermal and Statistical Physics Assignment 3 - Jan 16, 2008 1. Application of the Poisson distribution (see notes) . (a) Find the mean and the variance σ 2 of a random variable distributed like a Poisson distri- bution with parameter λ . Now consider a furnace that makes 1000 bricks per day, averaging 5 bad bricks per day. (b) What is the probability that, on a given day, no bad bricks are made? (c) What is the probability that, on a given day, 5 bad bricks are made? 2. Density of states in an ideal gas Consider the derivation provided in class that an ideal gas in equilibrium features
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Unformatted text preview: Ω( E ) ∝ V N E 3 N 2 (1) Consider a container of volume V with N particles at a given temperature T . The container then has a partition placed, so that the volume is separated in two halves. (a) Is the entropy before and after the placement of the partition the same? (b) If your answer to part (a) is negative, explain whether the conclusion is meaningful. The result of part (a) is known as the Gibbs paradox ....
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