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Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?
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Two metal spheres have radii r and 2r and they emit thermal radiation ...
Given: Two metal spheres of radii r and 2r respectively emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda.
To Find: The ratio of radiant energy emitted by the spheres per second.
Solution:
Step 1: Calculate the wavelength of the emitted radiation from the spheres
The wavelength of the maximum intensity of the emitted radiation is given by Wien's displacement law:
λ_max = b/T
Where b is Wien's constant and T is the temperature of the object emitting the radiation.
Since both spheres are emitting radiation with maximum intensity at different wavelengths, they must be at different temperatures.
Let the temperature of the first sphere be T1 and the temperature of the second sphere be T2.
Thus, we have:
λ1 = b/T1 and λ2 = b/T2
Step 2: Find the ratio of the radiant energy emitted by the spheres per second
The radiant energy emitted per unit time by a body at a temperature T is given by the Stefan-Boltzmann law:
E = σT^4
Where σ is the Stefan-Boltzmann constant.
Thus, the ratio of the radiant energy emitted per second by the two spheres is given by:
E2/E1 = (σT2^4)/(σT1^4) = (T2/T1)^4
Using the expressions for λ1 and λ2 from Step 1, we have:
(T2/T1)^4 = (λ2/λ1)^4 = (2Lambda/Lambda)^4 = 16
Thus, the ratio of the radiant energy emitted per second by the two spheres is 16.
Answer: The ratio of the radiant energy emitted per second by the two spheres is 16.
To Find: The ratio of radiant energy emitted by the spheres per second.
Solution:
Step 1: Calculate the wavelength of the emitted radiation from the spheres
The wavelength of the maximum intensity of the emitted radiation is given by Wien's displacement law:
λ_max = b/T
Where b is Wien's constant and T is the temperature of the object emitting the radiation.
Since both spheres are emitting radiation with maximum intensity at different wavelengths, they must be at different temperatures.
Let the temperature of the first sphere be T1 and the temperature of the second sphere be T2.
Thus, we have:
λ1 = b/T1 and λ2 = b/T2
Step 2: Find the ratio of the radiant energy emitted by the spheres per second
The radiant energy emitted per unit time by a body at a temperature T is given by the Stefan-Boltzmann law:
E = σT^4
Where σ is the Stefan-Boltzmann constant.
Thus, the ratio of the radiant energy emitted per second by the two spheres is given by:
E2/E1 = (σT2^4)/(σT1^4) = (T2/T1)^4
Using the expressions for λ1 and λ2 from Step 1, we have:
(T2/T1)^4 = (λ2/λ1)^4 = (2Lambda/Lambda)^4 = 16
Thus, the ratio of the radiant energy emitted per second by the two spheres is 16.
Answer: The ratio of the radiant energy emitted per second by the two spheres is 16.
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Two metal spheres have radii r and 2r and they emit thermal radiation ...
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Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?
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Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?.
Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two metal spheres have radii r and 2r and they emit thermal radiation with maximum intensity at wavelength Lambda and 2 Lambda respectively. the respective ratio of the radiant energy emitted by them per second will be?.
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