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Question: Answered & Verified by Expert
If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, the ratio of radiant energy received on earth to what it was previously, will be
PhysicsThermal Properties of MatterNEET
Options:
  • A 4
  • B 16
  • C 32
  • D 64
Solution:
2530 Upvotes Verified Answer
The correct answer is: 64
From Stefan law, the energy radiated by sun is given by. P=σeAT4, assuming e = 1 for sun.

In Ist case, P1=σe×4πR2×T4

In 2nd case, P2=σe×4π2R2×(2T4)

                        = σe×4πR2×T4×64=64P1

The rate at which energy is received by earth is,

E=P4πRSE2×AE

where AE = area of earth

RSE = distance between sun and earth

So, In Ist case, E1= P14πRSE2×AE

                        E2=P24πRSE2×AE=64E1

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