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…

In a typical combustion engine the workdone by a gas molecule is given by $\displaystyle \mathrm{W}=\alpha^2 \beta \mathrm{e}^{\frac{-\beta x^2}{k \mathrm{~T}}}$, where $\displaystyle x$ is the displacement, $\displaystyle k$ is the Boltzmann constant and T is the temperature. If $\displaystyle \alpha$ and $\displaystyle \beta$ are constants, dimensions of $\displaystyle \alpha$ will be :