Shulou(Shulou.com)11/24 Report--

It is a fact that everyone knows that the sun is very hot. "the red sun is burning like fire". But how hot it is, it is not enough to rely on adjectives, temperature is the last word.

Many astronomers want to know the temperature of the sun. In fact, one of the early motivations for determining the solar constant was to calculate the temperature of the sun.

Unfortunately, although the solar constants measured in the early days and the solar luminosity calculated from them are not far from the modern values (at least in the same order of magnitude), the theoretical basis for linking them to temperature has always been vacant. This theoretical "vacuum" led to a chaotic situation.

The methods of calculating temperature can be described as varied, from the non-existent "hot line" (heat-ray) to the inapplicable Newton cooling law (Newton's Law of Cooling). Take the projection results, from more than a thousand degrees to several million degrees, the sky difference, everything.

In order to encourage reliable research, in 1876, the French Academy of Sciences in Paris (Paris Academy of Sciences) set a prize for calculating the temperature of the sun, but to no avail. The prize was won by French physicist Jules Violle,1841-1923 with a very "unreliable" calculation of 15002500 ℃.

The theoretical basis of Joseph Stefan's calculation of solar temperature was not first obtained from experimental data by Austrian physicist Joseph Stefan,1835-1893 until 1879 and 1884, and then thermodynamically deduced by his compatriot Ludwig Boltzmann,1844-1906.

Boltzmann (Ludwig Boltzmann) they found that the radiant power of a blackbody per unit area (that is, the energy radiated per second) is proportional to the fourth power of the absolute temperature. This law is now called Stefan-Boltzmann law (Stefan-Boltzmann law), and the proportional coefficient is called Stefan-Boltzmann constant (Stefan-Boltzmann constant). Under the international system of units, the Stefan-Boltzmann constant is 5.67 × 10-8.

Although Stefan-Boltzmann law is aimed at blackbody, stellar radiation is mostly close to blackbody radiation, so this law is also approximately applicable to stellar radiation. With this law, there is a theoretical basis for calculating the surface temperature of the sun.

The method of calculation is simple: (under the absolute temperature scale) the fourth power of the surface temperature multiplied by the Stefan-Boltzmann constant is the radiation power per square meter of the sun's surface, multiplied by the sun's surface area. that is the total radiation power of the sun (that is, the total energy radiated per second), that is, the luminosity of my sun.

It is not difficult to obtain that the surface temperature of the sun (or rather, the effective temperature of the photosphere) is about 5800K (K is the temperature unit of the absolute temperature scale, and the 0 ℃ of the Celsius scale is about 273K).

In addition to the above method, we introduce a rough but interesting method.

In the above calculation, in addition to the Stefan-Boltzmann law, it is necessary to know the value of the Stefan-Boltzmann constant and the luminosity of the sun.

But in fact, as long as there is a fourth power relation given by Stefan-Boltzmann law, even if we do not know the magnitude of the Stefan-Boltzmann constant or even the luminosity of the sun, we can still calculate the surface temperature of the sun.

The method is simple: we know that the average temperature on the earth's surface is about 290K (that is, 17 ℃-a double average of region and time). Although it is easy to be ignored, a planet at this temperature will also radiate energy, and this energy can be approximately described by Stefan-Boltzmann law. Because it cannot glow itself like the sun, the energy on the earth's surface mainly comes from sunlight. In addition to sunlight, there are also contributions from the interior of the earth in the energy received on the surface of the earth. However, the average power of the latter is only 0.06W / m ~ 2, less than 1/10000 of the solar energy, which can be ignored in our calculation.

The earth can maintain its current surface temperature, which means that the energy it radiates outward is basically equal to the energy it receives from sunlight. Using this relationship, we can calculate the surface temperature of the sun.

The process of calculation is very simple. Readers might as well try it themselves. You will find that the Stefan-Boltzmann constant will be automatically eliminated in the process of calculation, and the result is about 6000K, which is not as accurate as the previous method, but it is not far from it.

The interesting thing about this method is that it uses the temperature of the planet to deduce the temperature of the star. But more interestingly, if we use it the other way around, we can also calculate the temperature of the planets at a certain distance from the temperature of the star. This feature is often used by astronomers to estimate the location and width of so-called habitable zones (habitable zone) around stars that have the potential to support life.

Of course, this calculation has great limitations. For example, it requires not only the existence of water and atmosphere on the planet that can make the temperature uniform, but also that atmosphere can not be as rich in Greenhouse Effect gas as Venus atmosphere.

Before the end of the game, let's hand out a small red packet-- introduce the spectrum type of the sun.

Shortly after the Stefan-Boltzmann law was published, the German physicist Wilhelm Wien,1864-1928 proved a law called Wien's law of displacement (Wien's displacement law) with thermodynamic methods.

Wilhelm Wien's law shows that the higher the surface temperature, the more the spectral distribution shifts to the shortwave direction, and the color shifts to the blue direction.

Taking advantage of this feature, astronomers classify stars into seven categories according to their spectral characteristics, which are marked as OMagol B, A, F, and K, respectively.

In the star spectrum diagram, the O type celestial body is blue, the surface temperature is the highest, above 33000K, the M type celestial body is red, and the surface temperature is the lowest, below 3700K.

Yellow celestial bodies like the sun are G-type, with surface temperatures between 5200 and 6000K. In each type, ten subtypes are divided according to the order of temperature from high to low, which is represented by the Arabic numeral 09, with 0 indicating the highest temperature and 9 indicating the lowest temperature.

The spectral type of the sun is G2, which is considered to be at a higher temperature in the G type. In some literature, the spectral type of the sun has been marked as G2 Ⅴ. The "Ⅴ" here means not the English letter "Ⅴ", but the Roman numeral "5". It comes from another classification rule, which means the main sequence star (that is, the star of prime age).

This article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Lu Changhai

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