Question

The equation of state of a gas is given by $\left(P+\frac{a}{V^{3}}\right)\left(V-b^{2}\right)=cT$, where $P$, $V$, $T$ are pressure, volume and temperature respectively, and $a$, $b$, $c$ are constants. The dimensions of $a$ and $b$ are respectively

• A. $[ML^8T^{-2}]$ and $[L^{3/2}]$
• B. $[ML^5T^{-2}]$ and $[L^3]$
• C. $[ML^5T^{-2}]$ and $[L^6]$
• D. $[ML^6T^{-2}]$ and $[L^{3/2}]$

Answer 1

Answer: (A)

$[P]=\left[\frac{a}{V^{3}}\right]$
$ \Rightarrow \left[M L^{-1} T^{-2}\right]=\frac{a}{\left[L^{3}\right]^{3}}$
$\Rightarrow a=\left[M L^{8} T ^{-2}\right]$
$[M]=\left[b^{2}\right] $
$\Rightarrow \left[L^{3}\right]=b^{2}$
$ \Rightarrow b=\left[L^{3 / 2}\right]$