Question

O NO:15
A quantity A appears in an equation,
Ae A/T
Pressure
B
I represent temperature, 'I frequency & boltzmann constant. Kinetic energy of a gas molecule is given
3
by KT What is the dimension of in length of b​

Answer 1

Given function is,

$B=\dfrac{a}{\beta}e^{-\frac{a b}{KT}}$

B = pressure

K = boltzmann constant

T = temperature

b = length

Kinetic energy of a gas molecule is 3 by KT.

In given equation $\dfrac{ab}{KT}$ should be dimensionless

We need to calculate the dimension of a

Using term of a

$a=\dfrac{KT}{b}$

Put the dimension formula

$\alpha=\dfrac{ML^2T^{-2}K^{-1}\times K}{L}$

$\alpha=MLT^{-2}$

We need to calculate the dimension of $\beta$

Using given function

$B=\dfrac{a}{\beta}$

$\beta=\dfrac{a}{B}$

Put the value of dimension of a and B

$\beta=\dfrac{MLT^{-2}}{ML^{-1}T^{-2}}$

$\beta=L^2$

Hence, The dimension of $\beta$ is L².