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A Spherical Ball a of Surface Area 20 Cm2 is Kept at the Centre of a Hollow Spherical Shell B of Area 80 Cm2. the Surface of a and the Inner Surface of B Emit as Blackbodies. - Physics

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Question

A spherical ball A of surface area 20 cm2 is kept at the centre of a hollow spherical shell B of area 80 cm2. The surface of A and the inner surface of B emit as blackbodies. Both A and B are at 300 K. (a) How much is the radiation energy emitted per second by the ball A? (b) How much is the radiation energy emitted per second by the inner surface of B? (c) How much of the energy emitted by the inner surface of B falls back on this surface itself?

Solution

Given:

Surface area of the spherical ball, SA = 20 cm2 = 20 × 10 -4 m-2

Surface area of the spherical shell, SB = 80 cm2 = 80 × 10-4 m2

Temperature of the spherical ball, TA = 300 K

Temperature of the spherical shell, T= 300 K

Radiation energy emitted per second by the spherical ball A is given by

EA = σSATA4

⇒EA 6.0 ×10-8× 20 × 10-4 × (300)4

⇒EA = 0.97 J

Radiation energy emitted per second by the inner surface of the spherical shell B is given by 

EB = σ SBTB4

⇒ EB  = 6.0 ×10 -8 × 80 × 10-4 × (300)4

⇒ EB = 3.76 J ≈  3.8 J

Energy emitted by the inner surface of B that falls back on its surface is given by

E = EB - E= 3.76 - 0.94

  ⇒ E = 2.82 J

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Solution A Spherical Ball a of Surface Area 20 Cm2 is Kept at the Centre of a Hollow Spherical Shell B of Area 80 Cm2. the Surface of a and the Inner Surface of B Emit as Blackbodies. Concept: Heat Transfer - Radiation.
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