Question

An object is at temperature of $400^{\circ} C$. At what approximate temperature would it radiate energy twice as first ? The temperature of surroundings may be assumed to be negligible :

• A. $200^{\circ} C$
• B. $200\, K$
• C. $800^{\circ} C$
• D. $800\, K$

Answer 1

Answer: (D)

As we radiation power
$P \propto T^{4}$
$\Rightarrow P_{1} \propto(400+273)^{4}$
and $P_{2} \propto(T)^{4}$
As $P_{2}=2 P_{1}$
$\Rightarrow (T)^{4}=2(673)^{4}$
$\Rightarrow T^{4}=4.1 \times 10^{11}$
$\Rightarrow T=\left(4.1 \times 10^{11}\right)^{1 / 4}$
$\Rightarrow T \approx 800\, K$