In a typical combustion engine the workdone by a gas molecule is given by $W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be :
$[{M^0}L{T^0}]$
$[ML{T^{ - 1}}]$
$[ML{T^{ - 2}}]$
$[{M^2}L{T^{ - 2}}]$
Solution
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