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Question: Answered & Verified by Expert
A sphere of density d, specific heat capacity c and radius r is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure. If the temperature difference is ΔT and surrounding temperature is T0, then rate of fall in temperature will be [Given that ΔT<<T0]
PhysicsThermal Properties of MatterNEET
Options:
  • A 12σT02ΔTrdc
  • B 12σT03ΔTrdc
  • C 12σT04ΔTrdc
  • D 12σΔTrdcT03
Solution:
2065 Upvotes Verified Answer
The correct answer is: 12σT03ΔTrdc
From Stefan's law

-ΔQΔt=σAT4-T04

mc-ΔTΔt=σAT0+ΔT4-T04

-ΔTΔt=σAT04mc1+ΔTT04-1

-ΔTΔt=σ4πr2T04d43πr3c1+4ΔTT0-1

as ΔT<<T0

-ΔTΔt=12σT03ΔTrdc

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