First slide

Radiation

Question

A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature. Then select the wrong statement.

Moderate

A

Both will emit equal amount of radiation per unit time in the beginning.
B

Both will absorb equal amount of radiation from the surroundings in the beginning.
C

The initial rate of cooling will be the same for two spheres.
D

The two spheres will have different temperatures at any time t > 0.

Solution

$m . s . (- \frac{dT}{dt}) = e . σ . A . (T^{4} - {T_{0}}^{4}) \Rightarrow - \frac{dT}{dt} \propto \frac{(T^{4} - {T_{0}}^{4})}{m}$
Initially T = T₁ for both spheres and for solid sphere ‘m’ is more . Hence option -(3) is right.

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