4) The equation of state of a gas expressed in terms of the following series $\infty$ $PV = nRT \sum_{i} B_i \left(\frac{n}{V}\right)^i$ where $B_i$'s are temperature dependent constants and called virial coefficients. Find the first three coefficients for the Berthelot equation of state. $\left(P + \frac{an^2}{TV^2}\right)(V - nb) = nRT$ where a, b are constants.
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Step 1: The Berthelot equation of state is given by PV = nRT + BnRT^2/P + CnRT^3/P^2, where B and C are the first and second virial coefficients, respectively. Show more…
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As we saw in class the equation of state of a gas can be expressed in a virial expansion as PV = nRT sum B_k(T) (n/V)^k where the B_k(T) are the virial coefficients. By expanding the "hard sphere" equation of state P = nRT / (V - nb) in a power series in (n/V) determine the first four virial coefficients.
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