If A represents density, B represents velocity, C represents specific heat capacity and D represents wavelength, then the quantity having the dimensions of product of A, B, C and D is

Options

A. Stefan's constant
B. Botltzmann's constant
C. thermal conductivity
D. universal gas constant

Answer

C

Explanation

According to the question,
Given, A=density, B=velocity, C=specific heat capacity and D=wavelength
So, dimensions of A, B, C and D are
`A=[ML^(-3)T^(0)], B=[M^(0)LT^(-1)], C=[M^(0)L^(2)T^(-2)K^(-1)] " and "D=[M^(0)LT^(0)]`
Hence dimension of ABCD =
`[ML^(-3)T^(0)][M^(0)LT^(-1)][M^(0)L^(2)T^(-2)K^(-1)][M^(0)LT^(0)]=[ML^((-3+1+2+1))T^((-1-2))K^(-1)]=[MLT^(-3)K^(-1)]`
or `" "ABCD=[MLT^(-3)K^(-1)]" ...(i)"`
Now, dimension of each given option,
(a) Stefan.s constant `=[ML^(0)T^(-3)K^(-4)]`
(b) Boltzmann.s constant `=[ML^(2)T^(-2)K^(-1)]`
(c) Thermal conductivity `=[MLT^(-3)K^(-1)]`
(d) Universal gas constant `=[ML^(2)T^(-2)K^(-1)]`
So, the dimension of product of A, B, C and D is same as dimensionof thermal conductivity. Hence, option (c) is correct