Question: The adjoining diagram shows the spectral energy density distribution $E_{\lambda}$of a black body ...

Question

The adjoining diagram shows the spectral energy density distribution $E_{\lambda}$ of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is

Answer 1

Solution

Area under curve represents the emissive power of the body $\frac{E_{T}}{E_{2000}} = \frac{A_{T}}{A_{2000}} = \frac{16}{1}$ (given) ….(i)

But from Stefan's law E ∝ T⁴ ∴ $\frac{E_{T}}{E_{2000}} = \left( \frac{T}{2000} \right)^{4}$ ...(ii)

From (i) and (ii) $\left( \frac{T}{2000} \right)^{4} = \frac{16}{1}$ ⇒ $\frac{T}{2000} = 2$

⇒ T = 4000K.

Question: The adjoining diagram shows the spectral energy density distribution \(E_{\lambda}\)of a black body ...

Solution