MHT CET · Physics · Thermal Properties of Matter
The sphere of radii \(8 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) are cooling. Their temperatures are \(127^{\circ} \mathrm{C}\) and \(527^{\circ} \mathrm{C}\) respectively. Find the ratio of energy radiated by them in the same time
- A \(0.06\)
- B \(0.5\)
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Total energy radiated from a body
Or
\(
\begin{array}{l}
Q=A \varepsilon \sigma T^{4} t \\
\frac{Q}{t} \propto A T^{4}
\end{array}
\)
\(
\frac{Q}{t} \propto r^{2} T^{4} \quad\left(\because A=4 \pi r^{2}\right)
\)
\(
\begin{aligned}
\frac{Q_{1}}{Q_{2}} &=\left(\frac{r_{1}}{r_{2}}\right)^{2}\left(\frac{T_{1}}{T_{2}}\right)^{4} \\
&=\left(\frac{8}{2}\right)^{2}\left[\frac{273+127}{273+527}\right]^{4}=1
\end{aligned}
\)
Or
\(
\begin{array}{l}
Q=A \varepsilon \sigma T^{4} t \\
\frac{Q}{t} \propto A T^{4}
\end{array}
\)
\(
\frac{Q}{t} \propto r^{2} T^{4} \quad\left(\because A=4 \pi r^{2}\right)
\)
\(
\begin{aligned}
\frac{Q_{1}}{Q_{2}} &=\left(\frac{r_{1}}{r_{2}}\right)^{2}\left(\frac{T_{1}}{T_{2}}\right)^{4} \\
&=\left(\frac{8}{2}\right)^{2}\left[\frac{273+127}{273+527}\right]^{4}=1
\end{aligned}
\)
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