Values of the virial coefficients B and C at a fixed temperature can be obtained from experimental

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Values of the virial coefficients B and C at a fixed temperature can be obtained from experimental PV T data by noting that

lim P-0 (V-x) P-0 (V) PV RT lim V lim P-0 (V0) PV - (RY - 1) = RT = 1 V PV RT -1 = B B -) = c V

a. Using these formulas, show that the van der Waals equation leads to the following expressions for the virial coefficients.

B=b- C = 6 a RT

b. The temperature at which 

PV lim v (P-1) = -1)=B=0 V P-0 RT (or V-00) is called the Boyle temperature. Show that for the van der Waals

where Tc is the critical temperature of the van der Waals fluid given by Eqs. 6.6-3. (For many real gases TBoyle is approximately 2.5Tc!)

Eqs. 6.6-3.

and a = Ze 9V RT 8 Using these results in Eq. 6.6-2a yields Pc = = b- V 3 a 276 By direct substitution we

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