JEE Main202126 Feb 2021Morning ShiftPhysicsUnits and DimensionsActual
In a typical combustion engine the workdone by a gas molecule is given by W = α 2 β e - β x 2 k T , where x is the displacement, k is the Boltzmann constant and T is the temperature. If α and β are constants, dimensions of α will be:
Options
- AMLT - 2
- BM 2 LT - 2
- CMLT - 1
- DM 0 LT 0
Correct answer
D. M 0 LT 0
Step-by-step solution
k T has dimension of energy β x 2 k T is dimensionless β L 2 = ML 2 T - 2 β = MT - 2 α 2 β has dimensions of work α 2 MT - 2 = ML 2 T - 2 α = M 0 LT 0