For the equation of state (Z=1+frac{B}{V}), show that [ alpha=frac{1}{P+frac{B R T}{V^{2}}} quad text { and }

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For the equation of state \(Z=1+\frac{B}{V}\), show that

\[ \alpha=\frac{1}{P+\frac{B R T}{V^{2}}} \quad \text { and } \quad \beta=\frac{1+\frac{B}{V}+\frac{T}{V} \frac{d B}{d T}}{T\left(1+\frac{2 B}{V}\right)} \]

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