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Q.

The work done by a gas molecule in an isolated system is given by, W=αβ2e-x2αkT , where x is the displacement k is the Boltzmann constant and T is the temperature, αand β are constants. Then the dimensions of β will be :

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a

M0LT0

b

M2LT2

c

MLT−2

d

ML2T−2

answer is C.

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Detailed Solution

x2αkT= dimensionless ⇒x2kT=α Using, v=3kTm⇒kT=v2⋅m3So,⇒α=x2mv2=L2M−1L−2T2=M−1T2Now, given that: work =α⋅β2⋅( dimensionless )So, dimensions of work is same as dimensions of α⋅β2⇒M1L1T−2⋅L1=M−1T2β2⇒β=M1L1T−2

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The work done by a gas molecule in an isolated system is given by, W=αβ2e-x2αkT , where x is the displacement k is the Boltzmann constant and T is the temperature, αand β are constants. Then the dimensions of β will be :