Question

Let σ and b be Stefan's constant and Wien's constant respectively, then dimensions of σb are ______.

Options

• [L¹ M^-1 T^-3 K^-3]

• [L¹ M¹ T³ K³]

• [L^-1 M¹ T^-3 K^-3]

• [L¹ M¹ T^-3 K^-3]

Answer 1

Let σ and b be Stefan's constant and Wien's constant respectively, then dimensions of σb are [L¹ M¹ T^-3 K^-3].

Explanation:

Dimensions of Stefan's constant,

[σ] = `([u])/(["A"]["T"]^4)`

`= (["ML"^2"T"^(-2)]//["T"])/(["L"^2"K"^4])`

= [MT^{- 3}K^{- 4}]

Dimensions of Wien's constant,

[b] = [λ][T] = [LK]

∴ Dimensions of [σb] = [MT^{- 3}K^{- 4}][LK]

= [L¹ M¹ T^-3 K^-3]