If A represents Boltzmann constant B represents Planck's constant and C represents speed of light in vacuum then the quantity having the dimensions of `A^(4)B^(-3)C^(-2)` is

Options

A. universal gas constant
B. specific heat capacity
C. stefan's constant
D. heat energy

Answer

C

Explanation

Dimension of Boltzmann.s constant
`A=(j)/(K) = (ML^(2)T^(-2))/(K^(1))=[ML^(2)T^(-2)K^(-1)]`
Dimension of Planck constant
`B=Js=[ML^(2)Y^(-1)]`
Dimension of speed of light, `C=[LT^(-1)]`
Desired dimension =`A^(4)B^(-3)C^(-2)`
`implies [ML^(2)T^(-2)K^(-1)]^(4)[ML^(2)T^(-1)]^(-3)[LT^(-1)]^(-2)`
`implies [M^(1)L^(0)T^(-3)K^(-4)] `
Stefan constant (`sigma` ) is given by
`E= sigmaT^(4) implies sigma=(E)/(T^(4))`
where E = energy per unit area per unit time and T = absolute temperature.
`implies "Dimension" sigma ==([ML^(2)T^(-2)])/[[L^(2)][T]K^(4)]`
`sigma =[ML^(0)T^(-3)K^(-4)]`
So desired dimension is of Stefan constant .