The Stefan-Boltzmann law describes the relationship between the total energy radiated per unit surface area of a black body and its absolute temperature. It states that the total energy radiated is proportional to the fourth power of the body's absolute temperature.
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The Stefan-Boltzmann law is represented by the equation: $E = \sigma T^4$, where $E$ is the total energy radiated per unit surface area, $\sigma$ is the Stefan-Boltzmann constant, and $T$ is the absolute temperature of the body.
The Stefan-Boltzmann constant, $\sigma$, has a value of approximately $5.67 \times 10^{-8}$ W/m$^2$K$^4$.
The Stefan-Boltzmann law is applicable to the study of the electromagnetic spectrum, as it describes the total energy radiated by a black body across all wavelengths.
Spectroscopy in astronomy utilizes the Stefan-Boltzmann law to determine the surface temperature of stars by analyzing their emitted radiation.
The Stefan-Boltzmann law is also used to calculate the radii of stars by combining the measured luminosity and surface temperature of the star.
Review Questions
Explain how the Stefan-Boltzmann law relates to the study of the electromagnetic spectrum in astronomy.
The Stefan-Boltzmann law describes the total energy radiated by a black body across all wavelengths of the electromagnetic spectrum. This is crucial in the study of the electromagnetic spectrum in astronomy, as it allows astronomers to determine the total energy output of celestial objects, such as stars, by analyzing their emitted radiation. The law provides a fundamental understanding of how the temperature of a black body, like a star, is directly related to the total energy it radiates, which is a key concept in the study of the electromagnetic spectrum in astronomy.
Describe how the Stefan-Boltzmann law is used in spectroscopy to measure the surface temperature of stars.
Spectroscopy in astronomy utilizes the Stefan-Boltzmann law to determine the surface temperature of stars. By analyzing the spectrum of light emitted by a star, astronomers can identify the specific wavelengths and intensities of the radiation. Using the Stefan-Boltzmann law, which relates the total energy radiated by a black body to its absolute temperature, astronomers can then calculate the surface temperature of the star. This is a crucial application of the Stefan-Boltzmann law in the field of spectroscopy, as it allows for the accurate measurement of stellar surface temperatures, which is essential for understanding the properties and evolution of stars.
Explain how the Stefan-Boltzmann law is used to measure the diameters of stars.
The Stefan-Boltzmann law can be used in combination with other astronomical observations to determine the diameters of stars. By measuring the total luminosity of a star and its surface temperature, the Stefan-Boltzmann law can be used to calculate the star's radius. The law states that the total energy radiated by a black body is proportional to the fourth power of its absolute temperature. Knowing the star's luminosity and temperature, the radius can be derived using the Stefan-Boltzmann equation. This application of the law is crucial in the field of stellar astrophysics, as it allows astronomers to accurately measure the physical sizes of stars, which is essential for understanding their structure, evolution, and place in the universe.
Black body radiation is the thermal electromagnetic radiation emitted from the surface of a perfect absorber and emitter of radiation, also known as a black body.
Planck's law describes the spectral radiance of electromagnetic radiation emitted from a black body in thermal equilibrium at a given temperature.
Absolute Temperature: Absolute temperature is a temperature scale where the lowest possible temperature is absolute zero, the point at which a system has the lowest possible thermal energy.