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Real Gas Equation

The equation ...

Question

The equation of state of a gas is given by $P (V - b) = n R T$ . If $1 mole$ of a gas is isothermally expanded from volume $V$ and $2 V$ , the work done during the process is

RT ln (\frac{2 V - b}{V - b})

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RT ln (\frac{V - b}{V})

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RT ln (\frac{V - b}{2 V - b})

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RT ln (\frac{V}{V - b})

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Solution

The correct option is A $RT ln (\frac{2 V - b}{V - b})$
Given, equation of state of gas
$P (V - b) = n R T$
Initial volume $(V_{i}) = V$
Final volume $(V_{f}) = 2 V$
Work done in an isothermal process,
$W = \int_{V_{i}}^{V_{f}} P d V$
$W = \int_{V}^{2 V} \frac{n R T}{V - b} d V = n R T ln (V - b) |_{V}^{2 V}$
For $1 mole$ ,
$W = RT ln (\frac{2 V - b}{V - b})$

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