Question

The equation of state of some gases can be expressed as $\left( P + \frac{a}{V^{2}} \right)(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,b,R$ are constants. The dimensions of $'a'$ are

• A. $ML^{5}T^{- 2}$
• B. $ML^{- 1}T^{- 2}$
• C. $M^{0}L^{3}T^{0}$
• D. $M^{0}L^{6}T^{0}$

Answer 1

Answer: (A)

$ML^{5}T^{- 2}$

Answer 2

By principle of dimensional homogenity

$\left\lbrack \frac{a}{V^{2}} \right\rbrack = \lbrack P\rbrack$

$\therefore$ $\lbrack a\rbrack = \lbrack P\rbrack\mspace{6mu}\lbrack V^{2}\rbrack = \lbrack ML^{- 1}T^{- 2}\rbrack\mspace{6mu} \times \lbrack L^{6}\rbrack$ = $\lbrack ML^{5}T^{- 2}\rbrack$