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A furnace emits radiation at 2000 K. Treating it as a black body radiation, calculate the monochromatic radiant flux density at 1 micron m wavelength
- a)5.81 * 10 7 W/m2
- b)4.81 * 10 7 W/m2
- c)3.81 * 10 7 W/m2
- d)2.81 * 10 7 W/m2
Correct answer is option 'D'. Can you explain this answer?
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A furnace emits radiation at 2000 K. Treating it as a black body radia...
(E) b = C 1 (Wavelength) -5/exponential [C 2/ (Wavelength) T] – 1.
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A furnace emits radiation at 2000 K. Treating it as a black body radia...
Calculation of Monochromatic Radiant Flux Density
Given parameters:
Temperature (T) = 2000 K
Wavelength (λ) = 1 micron = 1 × 10^-6 m
To calculate the monochromatic radiant flux density using the Planck's Law, we can use the formula:
Bλ(T) = (2hc^2/λ^5) × (1/(e^(hc/λkT)-1))
where,
Bλ(T) is the monochromatic radiant flux density
h is the Planck's constant (6.626 × 10^-34 J s)
c is the speed of light (2.998 × 10^8 m/s)
k is the Boltzmann's constant (1.381 × 10^-23 J/K)
Substituting the given values in the formula, we get:
Bλ(T) = (2 × 6.626 × 10^-34 × (2.998 × 10^8)^2 / (1 × 10^-6)^5) × (1/(e^((6.626 × 10^-34 × 2.998 ×10^8)/(1.381 × 10^-23 × 2000))-1))
Simplifying the above expression, we get:
Bλ(T) = 2.81 × 10^7 W/m^2
Therefore, the monochromatic radiant flux density at 1 micron wavelength is 2.81 × 10^7 W/m^2.
Hence, the correct answer is option D.
Given parameters:
Temperature (T) = 2000 K
Wavelength (λ) = 1 micron = 1 × 10^-6 m
To calculate the monochromatic radiant flux density using the Planck's Law, we can use the formula:
Bλ(T) = (2hc^2/λ^5) × (1/(e^(hc/λkT)-1))
where,
Bλ(T) is the monochromatic radiant flux density
h is the Planck's constant (6.626 × 10^-34 J s)
c is the speed of light (2.998 × 10^8 m/s)
k is the Boltzmann's constant (1.381 × 10^-23 J/K)
Substituting the given values in the formula, we get:
Bλ(T) = (2 × 6.626 × 10^-34 × (2.998 × 10^8)^2 / (1 × 10^-6)^5) × (1/(e^((6.626 × 10^-34 × 2.998 ×10^8)/(1.381 × 10^-23 × 2000))-1))
Simplifying the above expression, we get:
Bλ(T) = 2.81 × 10^7 W/m^2
Therefore, the monochromatic radiant flux density at 1 micron wavelength is 2.81 × 10^7 W/m^2.
Hence, the correct answer is option D.
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