Question

In the equation $\left(\frac{1}{P\beta }\right)=\frac{y}{k_{B}T}$, where $P$ is the pressure, $y$ is the distance, $k_B$ is Boltzmann constant and $T$ is the temperature. Dimensions of $\beta$ are:

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

Answer 1

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

From the given equation,

$\beta =\frac{k_{B}T}{yP}$

Dimension of $k_{B}T$ is that of energy=$\left[M{L}^2{T}^{-2}\right]$

Dimension of $y=\left[L\right]$

Dimension of $P$ is energy per unit volume=$\left[M{L}^{-1}{T}^{-2}\right]$

Thus dimension of $\beta =\left[M^0{L}^2{T}^0\right]$