1. Tardigrade
  2. Question
  3. Physics
  4. The van der Waals' equation of state for some gases can be expressed as: (P+(a/V2))(V-b)=R T where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a, b, and R are constants. The dimensional representation of a b / R T is

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Q. The van der Waals' equation of state for some gases can be expressed as:
$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$
where $P$ is the pressure, $V$ is the molar volume, and $T$ is the absolute temperature of the given sample of gas and $a, b$, and $R$ are constants.
The dimensional representation of $a b / R T$ is

Physical World, Units and Measurements

Solution:

$\left[\frac{a b}{V^{2}}\right]=[R T]$
$\Rightarrow\left[\frac{a b}{R T}\right]=\left[V^{2}\right]=\left[L^{6}\right]$