Assertion (A): Two spheres of same material have radius \(r_1\) and \(r_2\) respectively and temperature \(4000\text{ K}\) and \(2000\text{ K}\) respectively. The energy radiated per second by first sphere is more than second sphere.
Reason (R): In thermal conduction, energy is transferred by transference of particles of conducting body.
Solution:
The power radiated by a sphere is `\(P = e \sigma (4\pi r^2) T^4\)`. The ratio of powers is `\(frac{P_1}{P_2} = \frac{r_1^2 (4000\text{ K})^4}{r_2^2 (2000\text{ K})^4} = 16 \frac{r_1^2}{r_2^2}\)`.
For `\(P_1 > P_2\)`, we need `\(16 r_1^2 > r_2^2\)` or `\(r_1 > r_2/4\)`. This is not universally true (e.g., if `\(r_1 = r_2/5\)`). Thus, Assertion (A) is false. Reason (R) describes convection, not conduction. Conduction involves energy transfer through molecular vibrations and collisions, not by the bulk transference of particles. Therefore, Reason (R) is also false.
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