If the temperature of a hot body is increased by $50 \%$, then the increase in the quantity of emitted heat…
If the temperature of a hot body is increased by $50 \%$, then the increase in the quantity of emitted heat radiation will be approximately
- $125 \%$
- $200 \%$
- $300\%$
- $400 \%$
Solution
$\begin{aligned} & \text { Given: } \mathrm{T}_2=\mathrm{T}_1+\frac{50}{100} \mathrm{~T}_1 \\ & \mathrm{~T}_2=1.5 \mathrm{~T}_1\end{aligned}$
According to Stefan's law,
$\frac{\mathrm{Q}}{\mathrm{At}}=\sigma \mathrm{T}^4$
Percentage change in radiation is,
$\begin{aligned}
& \Delta \mathrm{E} \%=\frac{\mathrm{T}_2^4-\mathrm{T}_1^4}{\mathrm{~T}_1^4} \times 100 \\
& \Delta \mathrm{E} \%=\frac{(1.5)^4 \mathrm{~T}_1^4-\mathrm{T}_1^4}{\mathrm{~T}_1^4} \times 100 \\
& \Delta \mathrm{E} \% \approx 400 \%
\end{aligned}$
Asked in: MHT CET 2023 (11 May Shift 1)
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