Question

A spherical body radiates $300\text{W}$ power at $650\text{K}$. If the radius were halved and temperature doubled, then find the power radiated.

• A. $600\text{W}$
• B. $900\text{W}$
• C. $300\text{W}$
• D. $1200\text{W}$

Answer 1

The correct option is D $1200\text{W}$

Given,
Power radiated $\left(P_1\right)=300\text{W}$
Temperature $\left(T_1\right)=650\text{K}$
By stefan's law
Power radiated $\left(P_1\right)=A\sigma ϵT^4=\sigma \left(4\pi r^2\right)ϵT^4$
When radius is halved and temperature is doubled.
Power radiated $\left(P_2\right)=\sigma \left[4\pi {\left(\frac{r}{2}\right)}^2\right]ϵ(2T{)}^4$
$=4P_1$
$=4\times 300=1200\text{W}$