What should be the temperature of black body to emit radiant energy which is independent of the conditions in the surroundings?

temperature of black body should be more than zero

temperature of black body should be less than zero

temperature of black body should be equal to zero

Dimensional Formula of Boltzmann Constant and its Derivation

The dimensional formula of Boltzmann constant is given by,

[M¹L² T^-2 K^-1]

Where,

Boltzmann Constant (k) = Energy × [Temperature]^-1 . . . (1)

Since, Energy = M × a × displacement = [M¹ × M⁰L¹ T^-2 × L¹]

Therefore, the dimensions of energy = [M¹L² T^-2] . . . (2)

And, the dimensional formula of temperature = [M⁰ L⁰ T⁰ K¹] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Boltzmann Constant = Energy × [Temperature]^-1

Or, k = [M¹L² T^-2] × [M⁰ L⁰ T⁰ K¹]^-1 = [M¹L² T^-2 K^-1].

Therefore, the Boltzmann constant is dimensionally represented as [M¹L² T^-2 K^-1].

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