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Pressure depends on distance as, P = (al...

Pressure depends on distance as, `P = (alpha)/(beta)exp(-(alphaz)/(ktheta))`, where `alpha, beta` are constants, `z` is distance as , `k` is Boltzman's constant and `theta` is tempreature. The dimension of beta are

A

`M^(0) L^(0) T^(0)`

B

`M^(-1) L^(-1) T^(-1)`

C

`M^(0) L^(2) T^(0)`

D

`M^(-1) L^(1) T^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Unit of `K` is joules per kelvin or the dimensional formula of `K is [ML^(2) T^(-2) theta^(-1) ] . alpha z // k theta` should be dimensionless,
So, dimensional formula of `alpha = ([ML^(2) T^(-2)])/([L]) = MLT^(-2)`
Dimensional formula of `P = [ML^(-1) T^(-2)]`
rArr ` beta = [( alpha)/( P)] = ([MLT^(-2)])/( [ML^(-1)T^(-2)]) = M^(0) L^(0) T^(0)`
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