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  4. The temperature of a radiating body increases by 50 %. Then, the increase in the amount of radiation emitted will be approximately:

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Q. The temperature of a radiating body increases by $50\%.$ Then, the increase in the amount of radiation emitted will be approximately:

NTA AbhyasNTA Abhyas 2022

Solution:

Given that, $T_{i}$ and $T_{f}=1.5T_{i}$
So, $E \propto T^{4}$
$E_{i}=kT_{i}^{4}$
$E_{f}=kT_{i}^{4}\times 1.5^{4}=5.06T_{i}^{4}$
So, $\Delta E\%=\frac{T_{i}^{4} \left(\right. 5 . 06 \left.\right) - T_{i}^{4}}{T_{i}^{4}}\times 100=406\%$