Question

The SI unit and dimensions of Stefan's constant cr in case of Stefan's law of radiation is ______.

Options

• `"J"/("m"^3"s"^4), ["M"^1"L"^0"T"^-3"K"^-4]`

• `"J"/("m"^2"s"^4"K"), ["M"^1"L"^0"T"^-3"K"^3]`

• `"J"/("m"^3"s" "K"^4), ["M"^1"L"^0"T"^-3"K"^4]`

• `"J"/("m"^2"s" "K"^4), ["M"^1"L"^0"T"^-3"K"^-4]`

Answer 1

The SI unit and dimensions of Stefan's constant cr in case of Stefan's law of radiation is `underline("J"/("m"^2"s" "K"^4), ["M"^1"L"^0"T"^-3"K"^-4])`.

Explanation:

According to Stefan's law, energy emitted by a body per unit area per second is proportional to fourth power of the absolute temperature.

E = σ T⁴

where, E = energy emitted/area/second,

T = absolute temperature in kelvin

and σ = Stefan's constant ⇒ `sigma = "E"/"T"^4`

Unit of Stefan's constant

`=> ("J"//"m"^2"s")/"K"^4 = "J"//"m"^2 "s" "K"^4`

Dimensions of Stefan's constant,

`sigma = (["Energy"])/(["Area"] xx ["Time"] xx ["Temperature"]^4)`

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

`= ["M"^1 "L"^0 "T"^-3 "K"^-4]`