Van der Waals's equation of state is obeyed by real gases. For $n$ moles of a real gas,the expression will be :-

  • A
    $\left( \frac{P}{n} + \frac{na}{V^2} \right) \left( \frac{V}{n - b} \right) = RT$
  • B
    $\left( P + \frac{a}{V^2} \right) (V - b) = nRT$
  • C
    $\left( P + \frac{na}{V^2} \right) (nV - b) = nRT$
  • D
    $\left( P + \frac{n^2 a}{V^2} \right) (V - nb) = nRT$

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The relation between pressure exerted by an ideal gas $(P_{ideal})$ and observed pressure $(P_{real})$ is given by the equation
$P_{ideal} = P_{real} + \frac{an^2}{V^2}$
$(i)$ If pressure is taken in $N \ m^{-2}$,number of moles in $mol$,and volume in $m^3$,calculate the unit of $a$.
$(ii)$ What will be the unit of $a$ when pressure is in atmosphere and volume in $dm^3$?

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