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Q.

In a typical combustion engine the work done by a gas molecule is given by  W=α2βe−βx2kT, where x  is the displacement, k  is the Boltzmann constant and T is the temperature. If α  and β  are constants, dimensions of  α will be:

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a

M2LT−2

b

M0LT0

c

M L T−2

d

M L T−1

answer is B.

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Detailed Solution

Power of exponent is dimensionless.So,  βx2=kT=M1L2T−2⇒β=M1L0T−2And exponential term is also dimensionless.So, dimension of  α2β is same as dimension of work.⇒α2β=M1L2T−2⇒α2=M1L2T−2M1L0T−2=M0L2T0⇒[α]=M0L1T0
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