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An expression for a dimensionless quantity P is given by $P = \frac{α}{β} \log_{e} (\frac{K t}{β x})$ ; where $α$ and $β$ are constant, x is distance; K is Boltzmann constant and t is the temperature . Then the dimensions of $α$ will be

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$M L T^{- 2}$

$M L^{2} T^{- 2}$

$M L^{°} T^{- 2}$

$M ° L^{- 1} T °$

answer is C.

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Detailed Solution

$\frac{K t}{β x} = c o n s \tan t$

$∴ β = M L T^{- 2}$

$∴ α = β$

$∴ β = \frac{K t}{x} = \frac{M L^{2} T^{- 2} K^{- 1} K}{L}$

here p is dimensionless constant

$∴ α = M L T^{- 2}$

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