In a typical combustion engine the workdone by a gas molecule is...

$kT$ has dimension of energy

$\dfrac{\beta{x}^{2}}{kT}$ is dimensionless

\left[\beta\right]\left[{L}^{2}\right] = \left[{ML}^{2}{T}^{- 2}\right]

\left[\beta\right] = \left[{MT}^{- 2}\right]

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

\left[{\alpha}^{2}\right]\left[{MT}^{- 2}\right]$= \left[{ML}^{2}{T}^{- 2}\right]$

\left[\alpha\right]$= \left[{M}^{0}{LT}^{0}\right]$