Question

In the relation `P = (alpha)/(beta) e^((alpha Z)/(k theta))`, `P` is pressure, `Z` is height, `k` is Boltzmann constant and `theta` is the temperature. Find the dimensions of `alpha` and `beta`

Answer 1

Power of exponential is dimesnionless.
`(alpha Z)/(k theta)` is dimensionless.
`(alpha [L])/([ML^(2) T^(-2) K ^(-1)] [K])` is dimensionless.
`[alpha] = [MLT^(-2)]`
Dimensions of `(alpha)/(beta)` = Dimensions of `P`
`([MLT^(-2)])/(beta) = [ML^(01) T^(-2)]`
`[beta] = [L^(2)]`