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The spectral emissivity of an opaque surface at 800 K is approximated as
Black body radiation function values for a black surface at 800 K are as follows
Find the total emissivity of the surface?
  • a)
    0.4
  • b)
    0.45
  • c)
    0.6
  • d)
    0.52
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The spectral emissivity of an opaque surface at 800 K is approximated ...
By definition of total emissivity
ε = E/Eb
Where E =
∴ E =
∴ E =
∴ E = 0.3
E = 0.3 Eb,0➝3 + 0.8Eb,3➝7 + 0.1Eb,7➝ꝏ
E = 0.3 f3Eb + 0.8f3➝7Eb + 0.1f7➝ꝏE
E = [0.3f3 + 0.8(f7 -f3) + 0.1(1- f7)]Eb
∴ ε = [0.3f3 + 0.8(f7 - f3 ) + 0.1(1-f7)]
For T = 2400 μm-K
∴ f3 = 0.140256
Similarly for λ = 7 μm
λT = 5600 μm-K
∴ f7 = 0.701046
∴ ε = 0.3 x 0.140256 + 0.8
X (0.701046 - 0.140256) + 0.1 x (1 - 0.701046)
ε = 0.0420768 + 0.448632 + 0.0298954
ε = 0.5206042
≃ 0.52
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Most Upvoted Answer
The spectral emissivity of an opaque surface at 800 K is approximated ...
By definition of total emissivity
ε = E/Eb
Where E =
∴ E =
∴ E =
∴ E = 0.3
E = 0.3 Eb,0➝3 + 0.8Eb,3➝7 + 0.1Eb,7➝ꝏ
E = 0.3 f3Eb + 0.8f3➝7Eb + 0.1f7➝ꝏE
E = [0.3f3 + 0.8(f7 -f3) + 0.1(1- f7)]Eb
∴ ε = [0.3f3 + 0.8(f7 - f3 ) + 0.1(1-f7)]
For T = 2400 μm-K
∴ f3 = 0.140256
Similarly for λ = 7 μm
λT = 5600 μm-K
∴ f7 = 0.701046
∴ ε = 0.3 x 0.140256 + 0.8
X (0.701046 - 0.140256) + 0.1 x (1 - 0.701046)
ε = 0.0420768 + 0.448632 + 0.0298954
ε = 0.5206042
≃ 0.52
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Community Answer
The spectral emissivity of an opaque surface at 800 K is approximated ...
By definition of total emissivity
ε = E/Eb
Where E =
∴ E =
∴ E =
∴ E = 0.3
E = 0.3 Eb,0➝3 + 0.8Eb,3➝7 + 0.1Eb,7➝ꝏ
E = 0.3 f3Eb + 0.8f3➝7Eb + 0.1f7➝ꝏE
E = [0.3f3 + 0.8(f7 -f3) + 0.1(1- f7)]Eb
∴ ε = [0.3f3 + 0.8(f7 - f3 ) + 0.1(1-f7)]
For T = 2400 μm-K
∴ f3 = 0.140256
Similarly for λ = 7 μm
λT = 5600 μm-K
∴ f7 = 0.701046
∴ ε = 0.3 x 0.140256 + 0.8
X (0.701046 - 0.140256) + 0.1 x (1 - 0.701046)
ε = 0.0420768 + 0.448632 + 0.0298954
ε = 0.5206042
≃ 0.52
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The spectral emissivity of an opaque surface at 800 K is approximated asBlack body radiation function values for a black surface at 800 K are as followsFind the total emissivity of the surface?a)0.4b)0.45c)0.6d)0.52Correct answer is option 'D'. Can you explain this answer?
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