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Lecture 11a Ideal gas Number of states and density of states Partition functions q and Q Thermodynamic Functions Problem 12.9

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Single molecule translational energy states From quantum mechanics states of translational energy are enumerated by three integer numbers, l, m, n. Number of states within radius R, Number of states within energy

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Density of states Number of states with energy from 0 to Number of states with energy from to + d - g( )d, where g( ) density of states

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Partition function for translations q t - single particle By definition For a gas not close to T = 0, there is a huge number of states within a given energy range, thus the sum can be replaced with integral With substitutionthe integration gives

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Partition function Q - many particles For indistinguishable particles

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Thermodynamic functions show

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Thermodynamic functions II

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Problem 12.9 Determine the entropy change when two gases with number of moles N 1 and N 2, are initially in volumes V 1 and V 2, such that V 2 / V 1 = N 2 / N 1, are allowed to mix in the combined volume V 1 + V 2.

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Typically, it’s easier to work with the integrals rather than the sums

Typically, it’s easier to work with the integrals rather than the sums

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