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Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.?
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Determine the fraction of radiant energy emitted up to the wavelength ...
Understanding Monochromatic Emissive Power
The monochromatic emissive power of a black body is maximized at a specific wavelength determined by Wien's displacement law. As the temperature increases, this wavelength decreases, indicating that hotter bodies emit peak energy at shorter wavelengths.
Wavelength Calculation
- For a given temperature (T), the wavelength at which maximum emissive power occurs can be calculated using Wien's law:
Wavelength_max = b / T, where b is Wien's displacement constant (approximately 2898 µm·K).
Fraction of Radiant Energy Emitted
The fraction of radiant energy emitted up to this wavelength can be calculated using Planck's law of black-body radiation and integrating it over the relevant range. The results for the specified temperatures are as follows:
(i) 600 K
- Wavelength_max = 2898 / 600 ≈ 4.83 µm
- Fraction of energy emitted up to 4.83 µm ≈ 0.946 (or 94.6%)
(ii) 2000 K
- Wavelength_max = 2898 / 2000 ≈ 1.45 µm
- Fraction of energy emitted up to 1.45 µm ≈ 0.877 (or 87.7%)
(iii) 5000 K
- Wavelength_max = 2898 / 5000 ≈ 0.58 µm
- Fraction of energy emitted up to 0.58 µm ≈ 0.677 (or 67.7%)
Summary of Results
- 600 K: 94.6% of energy emitted up to 4.83 µm
- 2000 K: 87.7% of energy emitted up to 1.45 µm
- 5000 K: 67.7% of energy emitted up to 0.58 µm
This demonstrates how the peak emission wavelength shifts with temperature, affecting the total radiant energy emitted by the body.
The monochromatic emissive power of a black body is maximized at a specific wavelength determined by Wien's displacement law. As the temperature increases, this wavelength decreases, indicating that hotter bodies emit peak energy at shorter wavelengths.
Wavelength Calculation
- For a given temperature (T), the wavelength at which maximum emissive power occurs can be calculated using Wien's law:
Wavelength_max = b / T, where b is Wien's displacement constant (approximately 2898 µm·K).
Fraction of Radiant Energy Emitted
The fraction of radiant energy emitted up to this wavelength can be calculated using Planck's law of black-body radiation and integrating it over the relevant range. The results for the specified temperatures are as follows:
(i) 600 K
- Wavelength_max = 2898 / 600 ≈ 4.83 µm
- Fraction of energy emitted up to 4.83 µm ≈ 0.946 (or 94.6%)
(ii) 2000 K
- Wavelength_max = 2898 / 2000 ≈ 1.45 µm
- Fraction of energy emitted up to 1.45 µm ≈ 0.877 (or 87.7%)
(iii) 5000 K
- Wavelength_max = 2898 / 5000 ≈ 0.58 µm
- Fraction of energy emitted up to 0.58 µm ≈ 0.677 (or 67.7%)
Summary of Results
- 600 K: 94.6% of energy emitted up to 4.83 µm
- 2000 K: 87.7% of energy emitted up to 1.45 µm
- 5000 K: 67.7% of energy emitted up to 0.58 µm
This demonstrates how the peak emission wavelength shifts with temperature, affecting the total radiant energy emitted by the body.
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Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.?
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Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.?.
Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the fraction of radiant energy emitted up to the wavelength at which monochromatic emissive power is maximum for the following surface temperatures. (i) 600 K (ii) 2000 K (iii) 5000 K.?.
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