Question

Radius of two spheres of same material are 1 and 4 m respectively and their temperature are $4\times {10}^3$ and $2\times {10}^3$ K respectively. Then ratio of emitted energy of spheres per sec. will be

• A. 1 : 2
• B. 2 : 1
• C. 1 : 1
• D. 4 : 1

Answer 1

The correct option is C 1 : 1

$\begin{array}{c}\frac{U_1}{U_2}=\frac{A_1{T}_1^4}{A_2{T}_2^4}=\frac{E_1^2}{E_2^2}\cdot \left(\frac{T_1}{T_2}\right)=\frac{1}{16}\times \frac{{\left(4\times {10}^3\right)}^4}{{\left(2\times {10}^3\right)}^4}\\ =\frac{256}{16}\times \frac{1}{16}=\frac{1}{1}=1:1\end{array}$