1. Tardigrade
  2. Question
  3. Physics
  4. The equation of state of a real gas is given by ( p + ( a/ V2) ) (V - b) = RT where p, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the above equation is

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Q. The equation of state of a real gas is given by
$ \bigg( p + \frac{ a}{ V^2} \bigg) $ $(V - b) = RT$
where $p, V$ and $T$ are pressure, volume and temperature respectively and $R$ is the universal gas constant. The dimensions of the constant $a$ in the above equation is ______

IIT JEEIIT JEE 1997Physical World, Units and Measurements

Solution:

$ \bigg [ \frac{ a}{ V^2 } \bigg ] = [ p ] $
$\therefore [ a ] = [ p V^2 ] = [ ML^{ - 1} \, T^{ - 2} ] \, [ L^6 ] = [ ML^5 \, T^{ - 2} ] $