Thermal Physics: 17 flashcards
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1. What is a black body?
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An idealized object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
2. What is black body radiation?
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The electromagnetic radiation emitted by a black body when it is in thermal equilibrium with its surroundings.
3. State Kirchhoff's law of thermal radiation.
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For a body in thermal equilibrium, the emissivity equals its absorptivity at each wavelength: $\epsilon_\lambda = \alpha_\lambda$.
4. What is the Stefan-Boltzmann law?
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The total power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature: $P = \sigma T^4$.
5. What does Wien's displacement law state?
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The wavelength at which the emission is maximum is inversely proportional to the absolute temperature: $\lambda_{\text{max}} = \frac{b}{T}$, where $b \approx 2.898 \times 10^{-3} \, \text{m·K}$.
6. What is the value of the Stefan-Boltzmann constant $\sigma$?
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$\sigma \approx 5.67 \times 10^{-8} \, \text{W·m}^{-2}\text{·K}^{-4}$.
7. What is the ultraviolet catastrophe?
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The failure of classical physics (Rayleigh-Jeans law) to explain the observed black body spectrum at short wavelengths, predicting infinite energy.
8. How did Planck resolve the ultraviolet catastrophe?
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He assumed that energy is emitted or absorbed in discrete quanta: $E = h\nu$, where $h$ is Planck's constant.
9. What is Planck's radiation law?
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The spectral radiance of a black body at temperature $T$ is given by $B_\nu(T) = \frac{2h\nu^3}{c^2} \frac{1}{e^{h\nu/kT} - 1}$.
10. What is the Rayleigh-Jeans law?
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A classical approximation for black body radiation at long wavelengths: $B_\nu(T) \approx \frac{2\nu^2 kT}{c^2}$.
11. What is Wien's approximation?
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A short-wavelength approximation for black body radiation: $B_\nu(T) \approx \frac{2h\nu^3}{c^2} e^{-h\nu/kT}$.
12. What is the relation between frequency and wavelength for electromagnetic radiation?
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$c = \lambda \nu$, where $c$ is the speed of light.
13. What is emissivity?
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The ratio of the radiation emitted by a surface to the radiation emitted by a black body at the same temperature.
14. What is a perfect black body's emissivity?
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$\epsilon = 1$.
15. Give an example of a near-black body in nature.
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The Sun (approximately) or a cavity with a small hole (a practical black body).
16. How does the peak wavelength of a black body change as temperature increases?
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It decreases (shifts to shorter wavelengths) according to Wien's displacement law.
17. What is the total energy density of black body radiation proportional to?
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It is proportional to $T^4$: $u = a T^4$, where $a$ is the radiation constant.
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