TS EAMCET · Physics · Thermal Properties of Matter
Two solid spheres \(A\) and \(B\) made of the same material have radii \(r_A\) and \(r_B\) respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of \(A\) and \(B\) is :
- A \(\frac{r_A}{r_B}\)
- B \(\frac{r_B}{r_A}\)
- C \(\frac{r_A^2}{r_B^2}\)
- D \(\frac{r_B^2}{r_A^2}\)
Answer & Solution
Correct Answer
(B) \(\frac{r_B}{r_A}\)
Step-by-step Solution
Detailed explanation
\(\frac{4 \pi}{3} r^3 \rho c\left(-\frac{d T}{d t}\right)=\sigma 4 \pi r^2\left(T^4-T_0^4\right)\) \(\therefore\left(-\frac{d T}{d t}\right)=\frac{3 \sigma}{\rho r c}\left(T^4-T_0^4\right)=H\) (say) Ratio of rates of fall of temperature \(\frac{H_A}{H_B}=\frac{r_B}{r_A}\)
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