Question

In the relation $P =\frac{a}{\beta} e ^{-\frac{a z}{ k \theta}}, p$ is the pressure, $z$ the distance, $k$ is Boltzmann constant and $\theta$ is the temperature, the dimensional formula of $\beta$ will be

• A. $M^0\,L^2\,T^0$
• B. $ML^2\,T$
• C. $ML^0\,T^{-1}$
• D. $ML^2\,T^{-1}$

Answer 1

Answer: (A)

$M^0\,L^2\,T^0$

Answer 2

In given equation, $\frac{ az }{ k \theta}$ should be dimensionless
$\therefore a =\frac{ k \theta}{ z }$
$\Rightarrow a =\frac{ ML ^{2} T ^{-2} K ^{-1} \times K }{ L }= MLT ^{-2}$
And $p=\frac{a}{\beta}$
$\Rightarrow \beta=\frac{a}{p}=\frac{M L T^{-2}}{M L^{-1} T^{-2}}$
$=M^{0} \,L^{2}\, T^{0}$