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  4. An object is at temperature of 400° C. At what approximate temperature would it radiate energy twice as first ? The temperature of surroundings may be assumed to be negligible :

Q. 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 :

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Solution:

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

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