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A solid sphere and a hollow sphere of th...

A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature

A

both will emit equal amount of radiation per unit time in the beginning

B

both will absorb equal amount of radiation per second from the surroundings in the beginning

C

the initial rate of cooling will be the same for both the spheres

D

the two spheres will have equal temperatures at any instant

Text Solution

Verified by Experts

The correct Answer is:
A, B
Total radiation per second is given by
`P = e_rsigma T^4A`
Here, `e_r:sigma:T and A` all are same.
Hence, P will be same.
Same is the case with absorption per second.
Now, `P = ms (-(dT)/(dt))`
or Rate of cooling `(-(dT)/(dt)) = P/(ms) prop 1/m`
Mass of hollow sphere is less. So, its initial rate of cooling will be more.
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