# Lecture 3 - Virial Coefficients(16.5 Recall from the past...

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Lecture 3 1 Virial Coefficients (16.5) Recall from the past two lectures: Compressibility Factor PV Z RT == () For 1 , Z<1 at a given pressure, suggests a significant drop in V from 'ideal' behavior. cR TT T ≈≈ 1 Expand Z as a polynomial in ( ): V ρ ( ) 23 2 1 ... VV BT PV Z R TV V + + + This is the Virial Equation (virial - Latin for force). It was introduced in 1901 by Kamerlingh-Onnes for real gases. Notes : 1) Coefficients B 2V (T), B 3V (T) only depend on temperature for a given gas, not pressure. 2) B 2V (T)=B, B 3V (T)=C in other texts 2 nd virial coeff. 3 rd virial coeff.

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Lecture 3 2 ( ) ( ) 23 2 1. . . VV BT PV Z R TV V = =+ + + Notes cont. () 2v 3) - results from 2-body interactions, i.e interactions involving 2 atoms/molecules. V 3v 2 4) - comes from 3-body interactions V 5) 0, Boyle temperature BB T == This is where attractive and repulsive forces cancel and the gas behaves ‘ideally’ over an extended range in pressure. / 2 0 is related to potential between molecules: 21 B ur kT A N e r d r π ⎡⎤ =− u(r) is the isotropic (spherical) interaction potential between 2 molecules.
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## This note was uploaded on 04/01/2012 for the course CHEM 444 taught by Professor Gruebele,m during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lecture 3 - Virial Coefficients(16.5 Recall from the past...

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