The entropy of any system is given by, S = α 2 β ln μ kR J β 2 + 3 where α and…

The entropy of any system is given by, 
S=α2βlnμkRJβ2+3
where α and β are the constants. μ,J,k and R are number of moles, mechanical equivalent of heat, Boltzmann's constant and gas constant, respectively.
Take S=dQT
Choose the incorrect option from the following:
  1. α and J have the same dimensions.
  2. S,β,k and μR have the same dimensions.
  3. S and α have different dimensions.
  4. α and k have the same dimensions.

Solution

S=α2βℓnμkRJβ2+3
S=QT=Joule k-1
α2β=Joule k-1
PV=nRT  μkRJβ2=1

R= Joule k
⇒R= Joule k,k= Joule R
⇒β= Joule k
α2β= Joule k
⇒α= dimensionless

Asked in: JEE Main 2021 (20 Jul Shift 1)

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