Question

A hollow and a solid sphere of same material and having identical outer surface are heated under identical condition to the same temperature and allowed to cool down at the same time (both have same emissivity and absorptive power), then:

• A. In the beginning both will emit equal amount of radiation per unit time
• B. In the beginning both will absorb equal amount of radiation per unit time
• C. Both spheres will have same rate of fall of temperature $\left(\frac{dT}{dt}\right)$
• D. Both spheres will have equal temperatures at any moment

Answer 1

Answer: (A), (B)

The correct options are
A In the beginning both will emit equal amount of radiation per unit time
B In the beginning both will absorb equal amount of radiation per unit time

$u=e\sigma A{T}^4$
At initial condition
Both have same value of e, A and T
So both will emit equal amount of radiation per unit time
Same for absorption,
As, $u=ms\frac{dT}{dt}$
$e\sigma A{T}^4=ms\frac{dT}{dt}$
As mass of solid is more than mass of hollow
So, $\frac{dT}{dt}$ are not same.