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In a typical combustion engine the work ...

In a typical combustion engine the work done by a gas molecule is given `W=alpha^2betae^((-betax^2)/(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:

A

`[MLT^(-2)]`

B

`[MLT^(-1)]`

C

`[M^(0) LT^(0)]`

D

`[M^(2) LT^(-2)]`

Text Solution

Verified by Experts

The correct Answer is:
C
`(betax^2)/(KT)` is dimensionless
So, `KT = betax^2 implies [M^(-1)L^(2)T^(-2)]`
`beta=([M^1 L^2 T^(-2)])/([L^2])implies[M^1T^(-2)]`
`[M^(1) L^2 T^(-2)] = alpha^(2) [M^(1)T^(-2)]`
`alpha^2 =[L^2]`
`alpha = [L]`
`alpha = [M^(0)L^(1) T^(0)]`
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