Parallel rays of light of intensity I=912Wm−2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan constant σ=5.7×10−8Wm−2 K−4 and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

(a) In steady state Energy incident per second = Energy radiated per second ∴⇒⇒⇒⇒⇒T4−T04=40×1081πR2=σ(T4−T04)4πR2I=σ(T4−T04)4T4−81×108=40×108T4=121×108T≈330 K

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Parallel rays of light of intensity I=912 {Wm}^{-2} are incide

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Parallel rays of light of intensity $I = 912 Wm^{- 2}$ are incident on a spherical black body kept in surroundings of temperature $300 K$ . Take Stefan constant $σ = 5.7 \times 1 0^{- 8} Wm^{- 2} K^{- 4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

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330 K

660 K

990 K

1550 K

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Updated on: Dec 14, 2023

Book:

Waves And Thermodynamics (DC Pandey)

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Lucas Discussed

Parallel rays of light of intensity

I = 912 Wm^{- 2}

are incident on a spherical black body kept in surroundings of temperature

300 K

. Take Stefan constant

σ = 5.7 \times 1 0^{- 8} Wm^{- 2} K^{- 4}

and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

13 mins ago

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13 mins ago

Text solutionVerified

(a) In steady state Solution Image

Energy incident per second = Energy radiated per second

∴ \Rightarrow \Rightarrow \Rightarrow \Rightarrow \Rightarrow T^{4} - T_{0}^{4} = 40 \times 1 0^{8} 1 π R^{2} = σ (T^{4} - T_{0}^{4}) 4 π R^{2} I = σ (T^{4} - T_{0}^{4}) 4 T^{4} - 81 \times 1 0^{8} = 40 \times 1 0^{8} T^{4} = 121 \times 1 0^{8} T \approx 330 K

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Question Text	Parallel rays of light of intensity $I = 912 Wm^{- 2}$ are incident on a spherical black body kept in surroundings of temperature $300 K$ . Take Stefan constant $σ = 5.7 \times 1 0^{- 8} Wm^{- 2} K^{- 4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to
Updated On	Dec 14, 2023
Topic	Thermal properties of Matter
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	478
Avg. Video Duration	9 min

Text solutionVerified

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