At low pressure, the Vander Waals equation is reduced to:

Z = \frac{{p V}_{m}}{R T} = 1 - \frac{a}{V R T}

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Z = \frac{{p V}_{m}}{R T} = 1 + \frac{b}{V R T} p

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p V_{m} = R T

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Z = \frac{{p V}_{m}}{R T} = 1 - \frac{a}{R T}

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Solution

The correct option is C $Z = \frac{{p V}_{m}}{R T} = 1 - \frac{a}{V R T}$
Vander Waal equation
$(P + \frac{a}{V_{m}^{2}}) (V_{m} - b) = R T$
At low pressure, volume becomes large so, 'b' can be neglected from the equation. It reduced to,
$(P + \frac{a}{V_{m}^{2}}) V = R T$
$\Rightarrow \frac{P V_{m}}{R T} = R T - \frac{a}{V_{m}}$
$\Rightarrow Z = \frac{P V_{m}}{R T} = 1 - \frac{a}{R V T}$

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Similar questions

P (V_{m} - b) = R T

{(\frac{\partial Z}{\partial P})}_{T}

\frac{x b}{R T} .

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Z [= \frac{p V m}{R T}]

Z (= \frac{P V_{m}}{R T})

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P (V_{m} - b) = R T e x p (- a / R T V_{m})

P (V_{m} - b) = R T .

{(\frac{δ Z}{δ P})}_{T} is \frac{x b}{R T} .

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