Verified Solution • 2025–26 Session moderate

QJEEM21Ph3ffc: JEE Main 2021 Physics - Class 11 JEEM21Ph3ffc Solution: In a typical combustion engine the workdone by a gas molecule…

In a typical combustion engine the workdone by a gas molecule is given by W=α2βe−βx2kTW = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}} , where x is the displacement, k is the Boltzmann constant and T is the temperature. If α\alpha and β\beta are constants, dimensions of α\alpha will be :

Multiple Choice Options

  • A [M0LT0][{M^0}L{T^0}]
  • B [MLT−1][ML{T^{ - 1}}]
  • C [MLT−2][ML{T^{ - 2}}]
  • D [M2LT−2][{M^2}L{T^{ - 2}}]

Step-by-Step Verified Solution

kT has dimension of energy

βx2kT{{\beta {x^2}} \over {kT}} is dimensionless

[β][L2]=[ML2T−2][\beta ][{L^2}] = [M{L^2}{T^{ - 2}}]

[β]=[MT−2][\beta ] = [M{T^{ - 2}}]

α2β{\alpha ^2}\beta has dimensions of work

[α2][MT−2]=[ML2T−2][{\alpha ^2}][M{T^{ - 2}}] = [M{L^2}{T^{ - 2}}]

[α]=[M0LT0][\alpha ] = [{M^0}L{T^0}]

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring