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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Presentation transcript:

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

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

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

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

Partition function Q - many particles For indistinguishable particles

Thermodynamic functions show

Thermodynamic functions II

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.