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, find the value of temperature T.

• A. 3000K
• B. 4000 K
• C. 5000 K
• D. 6000 K

Answer 1

The correct option is B 4000 K

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 α T4

$\therefore \frac{E_T}{E_{2000}}={\left(\frac{T}{2000}\right)}^4$ ...(ii)

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

$\Rightarrow \frac{T}{2000}=2\Rightarrow T=4000k$.