Question

In the relation $P=\frac{a}{\beta }{e}^{-}\frac{az}{k\theta },p$ 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. $M{L}^{2}T$
• C. $M{L}^0{T}^{-1}$
• D. $M{L}^2{T}^{-1}$

Answer 1

The correct option is A $M^0{L}^2{T}^0$

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