# Kirchhoff's Law

Kirchhoff's Law is a rule discovered by famous German( Prussian) scientists.

## Discoveries of Gustav Kirchhoff

More often, Kirchhoff's laws imply regularities formulated for closed circuits and nodes of electrical circuits. In Russian-language literature, they prefer to call them rules. Act two. The first operates with currents, the second with voltages. The system of equations compiled with the help of formulas makes it possible to find network parameters that satisfy the requirements for the applicability of the computation data to it. The rules were formulated in 1845, this is not the only discovery of Kirchhoff.

In thermodynamics, another principle is known. He says that the ratio of body emissivity and absorption is constant for any materials, regardless of their nature, and is determined by two external parameters:

1. Wave frequency.
2. ambient temperature.

Closely related to the previous discovery is a fact from the life of a great scientist. In the 17th century, spectroscopy began to develop, Kirchhoff did not fail to leave his own trace in science, discovering three laws:

• The spectrum of radiation of a solid body is continuous. Kirchhoff introduced the concept of an absolutely black body, which has now become the key to the study of issues of energy transfer over a distance.
• Diluted gas emits in selected waves of the spectrum, with lengths depending on the state of quantum transitions of electrons of a substance. Lasers work on this basis.
• A hot solid surrounded by a cooled gas has a continuous emission spectrum minus individual frequencies absorbed by the enveloping cloud. The wavelengths depend on the quantum transitions of the substance circling around the object.

The scientist got to thermochemistry and showed that the thermal effect of the reaction depends on the change in the heat capacity of the system( before and after the process).The postulate is ranked among the main in the section of science. In the hydrodynamics of the Kirchhoff equation, I describe the motion of a solid body in an ideal fluid.

The first law of

## Kirghoff's laws for electrical circuits

1. The first Kirghoff's law states that the algebraic sum of the currents at the node of the circuit is zero. Outgoing currents are taken in calculations with a negative sign, incoming - with a positive one. Although the Russian-language literature says that the opposite is permissible. The essence is unchanged.
2. The second Kirghoff law is formulated for closed circuits. Claims that the sum of the voltage drops during a round trip is equal to all the EMFs encountered on the path. Moreover, the contours of any chain must be bypassed in a single direction: clockwise or counterclockwise.

The first equation needs no explanation. Sometimes it is difficult to understand in which direction the current flows, with a negative or positive sign you want to substitute in the formula. It is recommended to remember: the number of equations is one less than nodes. If there are doubts about the point, it is permissible to exclude it from consideration. In other situations, the sign of the potential difference at the ends of the problem area is analyzed. For this, the power sources acting here are added or subtracted( in physics, there are batteries).

According to generally accepted standards, a longer line in the graphical designation of a battery is considered a positive pole. The current flows from here according to the rules adopted in physics, although in practice everything happens the other way around - the movement is formed by negatively charged electrons. If the EMF acts on the site in different directions, they are subtracted, and the direction of the current is given the greatest.

Regarding the second law, the sign of the entry in the voltage drop formula at a specified area is determined by the direction of current flow. EMF are taken with the opposite sign, or stand on the other side of equality. As stated above, the cells need to be walked in one direction. Do not be embarrassed that in the formulas over the voltage and current is a point. This is the sign of a complex number.

Please note - given a simplified record of the second law. Here, all the EMFs are taken with the reverse of the sign actually present in the figure. There is another form of recording, where the voltage drop is separated from the EMF by the equal sign. Then the signs do not need to change. The last form of recording is given in the school course of physics and is shown in the picture just below the general one.

Kirchhoff Rule

## Kirchhoff's Law for Thermodynamics

Kirchhoff showed that the ratio of the emissivity and absorption capacity of a solid body does not depend on the substance, but is considered a function of frequency and temperature during thermodynamic equilibrium. Particularly interesting abstraction in this regard was an absolutely black body. This is an object that absorbs radiation incident on it. For him, the formula presented in the figure is simplified. The emissivity of an absolutely black body describes the function of the formula for other bodies. This hypostasis has a maximum determined by the law of displacement of wine and amplitude, determined by the first law of wine( a special case is Planck's formula).

The ratio of the emissivity and absorption capacity of any body is determined by the formulas for any temperatures and frequencies. Using a spectrometer, it is possible to estimate the emitted waves. This allows you to theoretically predict the absorption capacity of any object. In practice, such studies lead to the creation of objects like the invisible plane, which is hardly visible to locators.

From the law of energy conservation, it follows that total radiation equals absorption in thermodynamic equilibrium. This means that their ratio throughout the spectrum is equal to unity. Before the recognition of Kirchhoff's law, it has already been established that - the better the body absorbs energy, the more it radiates. Note that the spectral absorption and emission densities have a different shape. This is the great insight of Kirchhoff. The interaction is determined by the law of wine and on the graph looks like a mountain with the top shifted to the left relative to the center of the figure.

This allows you to understand where the radiation maximum is( at the crown).In all parts of the graph, where the line is below one, the body mainly absorbs energy. Due to the laws, it is possible to predict the temperature of the stars, for example, by color, and every blacksmith knows that the detail in the furnace has reached the condition only by the characteristic hue of the glow. These are practical manifestations of the laws of Wine and Kirchhoff.

The second interesting observation is the temperature. From the graphs of the density of the radiation can be seen, the higher the indicator, the more active the radiation goes. In particular, the stars do not absorb energy with a small exception, but mainly emit. In cold planets, the opposite process prevails. The body radiates if its temperature is above the environment. In other situations, energy absorption prevails.

Analogy of the Kirchhoff law

## Kirchhoff's work in the field of spectroscopy

Kirchhoff and Bunsen actively studied the emission spectra of chemical elements using the Fraunhofer invention. Using a prism or a diffraction grating, the light was decomposed into spectral components, and scientists observed the effect. So set the individual frequencies of a number of elements of the periodic table. These scientists laid the foundations of spectroscopy. In 1860, studies of eight elements and their unique spectra were published, among others:

• strontium;
• Lithium;
• potassium;
• Calcium;
• barium;
• sodium.

Kirchhoff and Bunsen showed that it is possible to carry out chemical analysis of substances using spectroscopy and discovered elements that were previously unknown in science( cesium - in ancient Rome "blue" in the spectrum of luminescence and rubidium - in ancient Rome "dark red").We established a relationship between the emission and absorption spectra, based on the characteristics of the sunlight showed selected properties of our body( the presence of iron, potassium, calcium, magnesium, nickel, chromium and sodium in the atmosphere of a star, the absence of lithium).Experiments were required to be carried out in the period of proximity of the Sun to the zenith: when the star sloped towards the horizon, the final effect of the contribution of the Earth’s atmosphere increased. As a result of the work, the Kirchhoff law for thermodynamics was born.

Using devices that decompose the spectrum into components, scientists have discovered a number of other laws mentioned above. The scientist used the Bunsen burner( Bunsen), injected sodium chloride or lithium chloride into the flame. As a result, a discrete spectrum was observed with the help of a diffraction grating, and it was established that the absorption occurs at the previous frequencies. Kirchhoff's conclusions:

1. A heated, gaseous body formed in a burner flame emits a discrete emission spectrum.
2. It has been established that there are no sodium element frequencies in solar radiation. The scientist folded the light of the day with the flame of the bunsen burner, the defect has been smoothed out. The radiation of sodium in the laboratory complemented the spectrum of the sun.
3. If later a spirit burner was taken for the experiment, the dark stripes became blacker. The conclusion followed that at a relatively low temperature of the gaseous body in the burner flame, it begins to absorb. So it is established that sodium is colder relative to the core of the solar atmosphere.

Experience with the burner

The scientist considered gas to be the best burner for the experiments. Since the luminosity of its flame is low and does not interfere with recording the spectrum of a gaseous body. Salts for the experiments were taken as clean as possible, repeated precipitation was carried out. A black box was used for observation, two telescopes were inserted into the walls of the device at an acute angle:

• saw the blackened back wall through the first observer;
• through the second light concentrated on the selected site.

A rotating prism helped to fix the desired segment of the spectrum opposite the observer's eyes. It is clear that this method is suitable only for visible radiation and does not affect the infrared and ultraviolet ranges.

## Other work

Kirchhoff devoted a lot of time to various branches of science. For example, I found an error in setting boundary conditions for solving differential equations for membrane oscillations presented to the public in 1811 by Sophie Germain. No need to think that the phrase Kirchhoff's law is narrowly limited by two rules, and one directly leads to Ohm's law formulated earlier.

Scientist G.Kirchhoff

The scientist is presented for the title of corresponding member of the Berlin Academy of Sciences in the Department of Mathematics, correspondent of the St. Petersburg Academy of Sciences. If in the first case the applicants mostly pointed to the gift in solving the problems of mechanics, our compatriots( Lenz and Jacobi) noted a great deal about Kirchhoff's merits in spectral analysis.

The scientist taught, possessed a phenomenal memory, by heart long lectures without deviations from the formal text. The feeling of scrupulousness helped immaculately to collect materials, and only a lack of technical equipment prevented, probably, from making new discoveries. For example, the scientist noted that one of the lines of the spectrum of calcium coincides with iron, but was unable to reliably tell whether an apparent coincidence. Now it is known that the wavelengths differ by 5-6 angstroms, but then it turned out to be impossible to say with absolute certainty.

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