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pentazoid

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## Homework Statement

Even at low density, real gases don't quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial expansion,

PV=nRT(1+B(T)/(V/n) + C(T)/(V/n)^2+...)

where functions B(T), C(T) and so on are called the virial coefficients.

Any proposed relation between P,V, and T , like the ideal gas law or the virial equationm is called an equation of state. Another famous equation of state , which is qualitative accurate even for dense fluids, is the van der waals equations

(P+an^2/V^2)(V-nb)=nRT

where a and b are constants that depend on the type of gas. Calculate the second and third virial coefficients(B and C) for a gas obeying the van der waals equation , and terms of a and b. (hint: The binomial expansion says that (1+x)^p=1+px+1/2p(p-1)x^2, provided that abs(px)<<1. Apply this approximation to the quantity [1-nb/V]^-1.)

## Homework Equations

## The Attempt at a Solution

(P+an^2/V^2)(V-nb)=nRT==> PV-Pnb-an^3b/V^2+an^2/V=nRT==> PV=nRT+Pnb+an^3/V^2-an^2/V ==> PV=nRT(1+Pnb/nRT-an/RTV+an^3b/nRTV^2) ==> PV=nRT(1+Pnb/PV-an/RTV+an^3b/nRTV^2)==> PV=nRT(1+nb/(V/n)-(a/RT)/(V/n)+(ab/RT)V^2/n^2). Therefore the coefficients of B and C are:

B(T)=(b-a/RT) and C(T)=ab/RT right?