The temperature of a black body is increased by $50 \%$, then the percentage increase in the rate of…
The temperature of a black body is increased by $50 \%$, then the percentage increase in the rate of radiation by the body is approximated
- $50 \%$
- $100 \%$
- $400 \%$
- $150 \%$
Solution
Rate of radiation $\mathrm{R} \propto \mathrm{T}^4$
$\begin{aligned}
& \therefore \frac{\mathrm{R}_2}{\mathrm{R}_1}=\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4=(1.5)^4 \approx 5 \\
& \therefore \mathrm{R}_2=5 \mathrm{R}_1
\end{aligned}$
Percentage increase $=\left(\frac{\mathrm{R}_2-\mathrm{R}_1}{\mathrm{R}_1}\right) \times 100=400 \%$
Asked in: MHT CET 2021 (23 Sep Shift 2)
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