First slide

Dimensions of physical quantities

Question

In the relation $P = \frac{α}{β} e^{- \frac{α Z}{k θ}}$ P is pressure, Z is the distance, k is Boltzmann constant and $θ$ is the temperature. The dimensional formula of $β$ will be

Moderate

A

$[M^{0} L^{2} T^{0}]$
B

$[M^{1} L^{2} T^{1}]$
C

$[M^{1} L^{0} T^{- 1}]$
D

$[M^{0} L^{2} T^{- 1}]$

Solution

In given equation, $\frac{α z}{k θ}$ should be dimensionless
$\begin{array}{l} ∴ [α] = [\frac{k θ}{z}] \\ \Rightarrow [α] = \frac{[M L^{2} T^{- 2} K^{- 1} \times K]}{[L]} = [M L T^{- 2}] \\ and P = \frac{α}{β} \\ \Rightarrow [β] = [\frac{α}{P}] = \frac{[M L T^{- 2}]}{[M L^{- 1} T^{- 2}]} = [M^{0} L^{2} T^{0}] \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App