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The Stefan-Boltzmann law, also known as Stefan's law, was formulated by Austrian physicist Josef Stefan in 1879 and derived by Austrian physicist Ludwig Boltzmann in 1884. The law describes the intensity of thermal radiation emitted by matter in terms of its temperature. It states that the total energy radiated per unit surface area per unit time (radiant exitance) is directly proportional to the fourth power of the temperature of the matter. In other words, as the temperature of an object increases, so does the amount of radiant energy it emits.
| Characteristics | Values |
|---|---|
| Name | Josef Stefan |
| Birth Year | 1835 |
| Death Year | 1893 |
| Deduction Year | 1877 |
| Basis | Tyndall's experimental measurements |
| Article | Über die Beziehung zwischen der Wärmestrahlung und der Temperatur (On the relationship between thermal radiation and temperature) |
| Publication | Bulletins from the sessions of the Vienna Academy of Sciences |
| Name | Ludwig Boltzmann |
| Birth Year | 1844 |
| Death Year | 1906 |
| Derivation Year | 1884 |
| Basis | Adolfo Bartoli's work |
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What You'll Learn
- The law was formulated by Austrian physicists Josef Stefan and Ludwig Boltzmann
- It calculates the temperature of emitting objects
- It is used in the study of thermodynamics and astrophysics
- It helps calculate the luminosity of celestial bodies
- It is one of the theoretical foundations of radiation thermometry theory
The law was formulated by Austrian physicists Josef Stefan and Ludwig Boltzmann
The Stefan-Boltzmann Law, also known as Stefan's Law, was formulated by Austrian physicists Josef Stefan and Ludwig Boltzmann. It describes the intensity of thermal radiation emitted by matter and expresses this in terms of that matter's temperature.
Josef Stefan first deduced the proportionality to the fourth power of absolute temperature in 1877, publishing his findings in an article titled 'On the relationship between thermal radiation and temperature' in the Bulletins from the sessions of the Vienna Academy of Sciences. Stefan's work was based on Tyndall's experimental measurements.
In 1884, Stefan's countryman and fellow physicist Ludwig Boltzmann derived the law from theoretical considerations, building on the work of Adolfo Bartoli. Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter.
The law states that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature. This relationship between radiation and temperature is expressed as:
> E = σT4
Where E is the radiant heat energy emitted from a unit area in one second, T is the absolute temperature in kelvins, and σ (sigma) is the Stefan-Boltzmann constant.
The Stefan-Boltzmann Law is widely used in the study of thermodynamics and astrophysics, helping scientists calculate the luminosity of celestial bodies and understand the effects of rising temperatures on Earth due to greenhouse gases.
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It calculates the temperature of emitting objects
The Stefan-Boltzmann law, also known as Stefan's law, describes the intensity of thermal radiation emitted by matter in terms of its temperature. It was formulated by Austrian physicist Josef Stefan in 1879 and derived theoretically by Austrian physicist Ludwig Boltzmann in 1884.
The law states that the total radiant heat power emitted from a surface is directly proportional to the fourth power of its absolute temperature. This relationship can be expressed as E = σT^4, where E is the radiant heat energy emitted from a unit area in one second, T is the absolute temperature in Kelvin, and σ is the Stefan-Boltzmann constant.
The Stefan-Boltzmann law can be applied to calculate the temperature of emitting objects, including the Sun and Earth. For example, using the law, Stefan determined the temperature of the Sun's surface, obtaining a value of 5430 °C or 5700 K. This was the first sensible value for the Sun's temperature, as previous estimates ranged from as low as 1800 °C to as high as 13,000,000 °C.
Additionally, the law can be used to calculate the effective temperature of the Earth by equating the energy received from the Sun with the energy radiated by the Earth. This calculation takes into account the Earth's distance from the Sun and the irradiance or power per unit area received.
The Stefan-Boltzmann law is a fundamental concept in physics and has applications in various fields, including radiation thermometry theory and the study of blackbody radiation. It provides a quantitative expression of the relationship between radiation and temperature, helping us understand how the amount of radiant energy emitted by an object increases rapidly with temperature.
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It is used in the study of thermodynamics and astrophysics
The Stefan-Boltzmann law, also known as Stefan's law, describes the intensity of thermal radiation emitted by matter in relation to its temperature. It is used in the study of thermodynamics and astrophysics in several ways.
Thermodynamics
The law is used in thermodynamics to determine the temperature of a body in relation to its radiation output. The law states that the magnitude of the radiation output of an object is directly proportional to the fourth power of its surface temperature. In other words, as the temperature of an object increases, the amount of radiant energy it emits increases rapidly. This relationship is expressed as a formula for radiance as a function of temperature, with radiance measured in watts per square metre per steradian (W⋅m−2⋅sr−1).
The Stefan-Boltzmann law also considers the concept of emissivity, which is the ability of a body to emit thermal radiation. Emissivity is generally between zero and one, with an emissivity of one corresponding to a black body, which is a perfect absorber and emitter of radiation. The law can be applied to all matter, provided that the matter is in a state of local thermodynamic equilibrium (LTE) so that its temperature is well-defined.
Astrophysics
In astrophysics, the Stefan-Boltzmann law is used to determine the temperature of celestial bodies, such as stars and black holes. Astronomers can use the law to infer the radii of stars by treating the emitted energy as blackbody radiation. The law also allows for the calculation of the effective temperature of the Earth by equating the energy received from the Sun with the energy radiated by the Earth.
Additionally, the law can be used to determine the temperature of the Sun's surface. Stefan used his law to infer from the data of Jacques-Louis Soret that the energy flux density from the Sun is 29 times greater than that of a warmed metal lamella. By considering the absorption of the Earth's atmosphere, Stefan obtained a value of 5430 °C or 5700 K for the temperature of the Sun, which was the first sensible value.
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It helps calculate the luminosity of celestial bodies
The Stefan-Boltzmann Law, also known as Stefan's Law, describes the intensity of thermal radiation emitted by matter in terms of its temperature. It was formulated by Austrian physicists Josef Stefan in 1879 and Ludwig Boltzmann in 1884. The law is a powerful tool with a wide range of applications in astrophysics, engineering, and environmental science.
The law states that the total energy radiated per unit surface area of a blackbody across all wavelengths per unit time is proportional to the fourth power of the blackbody's absolute temperature. This law helps scientists calculate the luminosity of celestial bodies such as stars, planets, and galaxies. It also aids in understanding the thermal radiation emitted by various celestial bodies, including planets and asteroids.
The Stefan-Boltzmann Law is used to estimate the luminosity of stars by relating their size, temperature, and luminosity. It applies to any object emitting a thermal spectrum, including the Sun and other stars. By knowing the surface temperature and radius of a star, the Stefan-Boltzmann Law can be used to estimate its luminosity. This is calculated using the formula:
> L = 4π (6.96 x 10^8)^2 x 5.670367 x 10^-8 x (5778)^4 ≈ 3.846 x 10^26 W
Where L is the luminosity, and the numerical constant 5.67 x 10^-8 is the Stefan-Boltzmann constant. This calculation is consistent with observed values, demonstrating the applicability of the law in astrophysics.
In addition to its applications in astrophysics, the Stefan-Boltzmann Law is also used in engineering to design more power-efficient systems. By comparing the surface temperatures for various materials, engineers can design systems that do not require active cooling.
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It is one of the theoretical foundations of radiation thermometry theory
The Stefan-Boltzmann Law, also known as Stefan's Law, describes the intensity of thermal radiation emitted by matter in terms of that matter's temperature. It is one of the theoretical foundations of radiation thermometry theory. The law was formulated by Austrian physicists Josef Stefan and Ludwig Boltzmann.
Stefan's work in this area began in 1877, when he deduced the proportionality to the fourth power of absolute temperature on the basis of Tyndall's experimental measurements. He published his findings in an article titled 'Über die Beziehung zwischen der Wärmestrahlung und der Temperatur' ('On the relationship between thermal radiation and temperature') in the Bulletins from the sessions of the Vienna Academy of Sciences.
Boltzmann derived the law from theoretical considerations in 1884, drawing upon the work of Adolfo Bartoli. Following Bartoli, Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter.
The Stefan-Boltzmann Law is used to determine the temperature of various celestial bodies. For example, with his law, Stefan determined the temperature of the Sun's surface. Astronomers can also use the law to infer the radii of stars.
The law is expressed as E = σT^4, where E is the radiant heat energy emitted from a unit area in one second (the power from a unit area), T is the absolute temperature in kelvins, and σ is the Stefan-Boltzmann constant.
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Frequently asked questions
The Stefan-Boltzmann Law was created by Josef Stefan and Ludwig Boltzmann.
Josef Stefan was an Austrian physicist who formulated the law in 1879 as a result of his experimental studies.
Ludwig Boltzmann was an Austrian physicist who derived the law in 1884 from thermodynamic considerations.
