Question

The work done by a gas molecule in an isolated system is given by, W = α.β².e-x² / αkT, where x is the displacement, k is the Boltzmann constant and T is the temperature.α and β are constants. Then the dimensions of β will be

a. [M⁰LT⁰]

b. [M²LT²]

c. [MLT^–2]

d. [ML²T^–2]

Answer 1

The correct option is c) MLT^-2 

we knnow that ,x² / α.k.T = dimensionless

[x² / α.k.T ] = [M⁰L⁰T⁰]

[α] = [L² / k.T]

⇒ [κ] = [M¹L²T^-2K^-1]

[T] = [K]

⇒ [α] = [L² / M¹L²T^-2K^-1× K] ⇒ [α] = [M^-1T²]

⇒ ω = α.β²

⇒ [M¹L¹T^-2][L^-1] / [M^-1T²] = [β²] = [M²L²T^-4]

[β] = [MLT^-2]