Question

The entropy of any system is given by `S = alpha^2betaIn[(mukR)/(Jbeta^2) + 3]` Where α and β are the constants µ J, k, and R are no. of moles, the mechanical equivalent of heat, Boltzmann constant, and gas constant respectively. `["take S" = (dQ)/T]`

Choose the incorrect option from the following.

विकल्प

• S, β, k, and µR have the same dimensions.

• α and J have the same dimensions.

• S and α have different dimensions.

• α and k have the same dimensions.

Answer 1

α and k have the same dimensions.

Explanation:

`S = alpha^2betaIn[(mukR)/(Jbeta^2) + 3]` ......(i)

`(mukR)/(Jbeta^2)` → dimensionless

`S = Q/T = "Joule"/"Kelvin"`

⇒ [S] = `[ML^2T^-2]/theta = ML^2T^-2theta^-1`

Ideal gas equation, PV = µRT

µR = `"PV"/T`

[µR] = ML²T^-2θ^-1

k → Boltzmann constant [k] = ML²T^-2θ^-1

J → dimensionless constant