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Unformatted text preview: 1 Chemistry 350 Term Test Supplement Winter 2011 Submit by Midnight Monday Evening March 14 Instructor: R.J. Le Roy Issued Sunday March 13, 2011 1. Our derivation of the the Boltzmann distribution function showed that the population a i of a given state i with energy i was proportional to e- i (i.e., to e- i / ( k B T ) ): a i = B e- i (a) For a system of N particles, derive an expression for the proportionality constant B in our expression for a i . (b) For this N-particle system, derive an expression for the thermodynamic internal energy U in terms of its molecular partition function. 2. The Sackur-Tetrode equation for the entropy of an ideal gas of N a atoms of mass m a occupying a volume V a may be written in the form S a = N a k B ln ( 2 m a k B T h 2 3 / 2 e 5 / 2 V a N a ) (a) If this system is heated from temperature T 1 to T 2 , determine the value of the ratio ( S ) V / ( S ) P , the ratio of the entropy change for this process occurring at constant volume to that if the pro-...
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