JEE Main202120 Jul 2021Morning ShiftPhysicsThermodynamicsActual
The entropy of any system is given by, S = α 2 β ln μ kR J β 2 + 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 = d Q T Choose the incorrect option from the following:
Options
- Aα and J have the same dimensions.
- BS , β , k and μ R have the same dimensions.
- CS and α have different dimensions.
- Dα and k have the same dimensions.
Correct answer
D. α and k have the same dimensions.
Step-by-step solution
S = α 2 β ℓ n μ k R J β 2 + 3 S = Q T = Joule   k - 1 α 2 β = Joule   k - 1 P V = n R T    μ k R J β 2 = 1 R =  Joule  k ⇒ R =  Joule  k , k =  Joule  R ⇒ β =  Joule  k α 2 β =  Joule  k ⇒ α = dimensionless