Q. The Vander Waal’s equation of state for real gases is given as $\left( P + \frac{a}{V^{2}} \right)(V - b) = nRT$ which of the following terms has dimensions different from that of energy
A) $PV$
B) $\frac{a}{V^{2}}$
C) $\frac{ab}{V^{2}}$
D) $bP$
Explanation
$PV =$[energy] Vander Waal’s equation is $\left( P + \frac{a}{V^{2}} \right)(V - b) = nRT$ The dimensions of $\frac{a}{V^{2}}$ should be that of $P$ and $b$ is that of volume Work done (or energy) should have the dimensions of $PV$ $\therefore\ \left\lbrack \frac{a}{V^{2}} \times b \right\rbrack =$ [Energy] $\lbrack bP\rbrack =$ [Energy] $\left\lbrack \frac{a}{V^{2}} \right\rbrack = \lbrack P\rbrack$ is having dimensions different from energy
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.