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  4. In Vander Waals equation [ P +( a / V 2)][ V - b ]= RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants ( a / b ) is dimensionally equal to:

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Q. In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{ a }{ b }$ is dimensionally equal to:

JEE MainJEE Main 2022Physical World, Units and Measurements

Solution:

By principle of homogenity
${[ P ]=\left[\frac{ a }{ v ^{2}}\right] \text { and }[ b ]=[ v ]}$
$\Rightarrow\left[\frac{ a }{ b }\right]=[ PV ]( C )$