Stefan-Boltzmann Law Stefan Batory Stefan Banach Stefano Benni

Thus at 100 K the energy flux density is 5.67 W/m², at 1000 K 56.7 kW/m², etc.

The law was experimentally discovered by Jožef Stefan ( 1835- 1893) in 1879 and theoretically derived in the frame of the thermodynamics by Ludwig Boltzmann ( 1844- 1906Events January 8 Landslide in Haverstraw, New York kills 20 January 31 Earthquake in Ecuador (8. 6 in Richter scale) February 11 Pope Pius X publishes the encyclical Vehementer nos''. February 15 Representatives of the Labour Representation Committee in t) in 18841884 is a leap year starting on Tuesday (click on link to calendar). Events January 4 The Fabian Society is founded in London. February 1 Edition one of the Oxford English Dictionary is published. March 13 The siege of Khartoum, Sudan begins (ends on Janu. Boltzmann treated a certain ideal heat engineA heat engine performs the conversion of heat energy to work by exploiting the temperature gradient between a hot " source" and a cold " sink". Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. with the lightLight is electromagnetic radiation with a wavelength that is visible to the eye, or in a more general sense, any electromagnetic radiation in the range from infrared to ultraviolet. The three basic dimensions of light (and of all electromagnetic radiation as a working matter instead of the gas. This law is the only physical law of nature named after a Slovene physicistA physicist is a scientist trained in physics. Physicists are employed by universities as professors, lecturers, researchers, and by laboratories in industry. Employment as a professional physicist generally requires a doctoral degree. However, many peopl. Today we can derive the law from Planck's law of black body radiationIn physics, the intensity spectrum of electromagnetic radiation from a black body at temperature T is given by the Planck's law of black body radiation : where: :ν is the frequency I ν) is the amount of energy per unit time per unit surface per unit:

and is valid only for ideal black objects, the perfect radiators, called blackbodies. Stefan published this law on March 20March 20 is the 79th day of the year in the Gregorian Calendar (80th in Leap years). There are 286 days remaining. Events 1413 Henry V becomes King of England. 1602 The Dutch East India Company is established. 1739 Nadir Shah occupies Delhi in India and s in the article 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.

1 Temperature of the Sun

With his law Stefan also determined the temperature of the Sun's surface. He learnt from the data of Charles Soret ( 1854– 1904) that the energy flux density from the Sun is 29 times greater than the energy flux density of a warmed metal lamella. A round lamella was placed at such a distance from the measuring device that it would be seen at the same angle as the Sun. Soret estimated the temperature of the lamella to be circa 1900 °C to 2000 °C. Stefan surmised that 1/3 of the energy flux from the Sun is absorbed by the Earth's atmosphere, so he took for the correct Sun's energy flux a value 3/2 times greater, namely 29 × 3/2 = 43.5. Precise measurements of atmospheric absorption were not made until 1888 and 1904. The temperature Stefan obtained was a median value of previous ones, 1950 °C and the absolute thermodynamic one 2200 K. As 2.57⁴ = 43.5, it follows from the law that the temperature of the Sun is 2.57 times greater than the temperature of a lamella, so Stefan got a value of 5430 °C or 5700 K (modern value is 5780 K). This was the first sensible value for the temperature of the Sun. Before this, values from circa 1800 °C to 13,000,000 °C were claimed. The first value of 1800 °C was determined by Claude Servais Mathias Pouillet ( 1790- 1868) in 1838 using the Dulong-Petit law. Pouilett also took just half the value of the Sun's correct energy flux. Perhaps this result reminded Stefan that the Dulong-Petit law could break down at large temperatures. If we collect the Sun's light with a lens, we can warm a solid to much higher temperature than 1800 °C.

The Stefan-Boltzmann law is an example of a power law.

2 Examples

With the Stefan-Boltzmann law, astronomers can easily infer the radii of stars. The law is also met in the thermodynamics of black holes in so called Hawking radiation.

Similarly we can calculate the temperature of the Earth T_E by equating the energy received from the Sun and the energy transmitted by the Earth:

where T_S is the temperature of the Sun, r_S the radius of the Sun and a₀ astronomical unit, giving 6°C.

Summarizing: the surface of the Sun is 21 times as hot as that of the Earth, therefore it emits 190,000 times as much energy per square metre. The distance from the Sun to the Earth is 215 times the radius of the Sun, reducing the energy per square metre by a factor 46,000. Taking into account that the cross-section of a sphere is 1/4 of its surface area, we see that there is equilibrium (342 W per m² surface area, 1,370 W per m² cross-sectional area).

This shows roughly why T ~ 300 K is the temperature of our world. The slightest change of the distance from the Sun or atmospheric conditions might change the average Earth's temperature.

Some physicists have criticised Stefan for using a theoretically unsound method to determine the law. It is true that he was helped by some fortunate coincidences, but this does not mean that he found the law blindly.

Thermodynamics

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Home > Stefan-Boltzmann law

1 Temperature of the Sun

2 Examples

Topics: Stefan-Boltzmann Law, Stefan Batory, Stefan Banach, Stefano...