JEE Main202124 Feb 2021Morning ShiftPhysicsUnits and DimensionsActual
The work done by a gas molecule in an isolated system is given by, W = α β 2 e - x 2 α k T , 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:
Options
- AM 2   L   T 2
- BML 2   T - 2
- CMLT - 2
- DM 0   L   T 0
Correct answer
C. MLT - 2
Step-by-step solution
x 2 α k T → dimensionless ⇒ α = x 2 k T = L 2 ML 2   T - 2 = M - 1   T 2 Now W = α β 2 β = ML 2   T - 2 M - 1   T 2 = M 1   L 1   T - 2