Purpose of work

Acquaintance with the methodology for experiments to determine the degree of black surface of the body.

Development of experimental skills.

The task

Determine the degree of black ε and the radiation coefficient from the surfaces of 2 different materials (painted copper and polished steel).

Set the dependence of changes in the degree of black on the surface temperature.

Compare the value of the degree of black of painted copper and polished steel among themselves.

Theoretical administration

The thermal radiation is the process of transferring thermal energy by means of electromagnetic waves. The amount of heat transmitted by radiation depends on the properties of the emitting body and its temperature and does not depend on the temperature of the surrounding bodies.

In the general case, the thermal stream falling on the body is partially absorbed, partially reflected and partially passes through the body (Fig. 1.1).

Fig. 1.1. Radiant Energy Distribution Scheme

(2)

where - heat flow falling on the body,

- the amount of heat absorbed by the body,

- the amount of heat reflected by the body,

- The amount of heat passing through the body.

We divide the right and left parts on the heat flow:

Values
it is called respectively: absorbing, reflective and body transduction capacity.

If a
T.
. The entire heat flux falling on the body is absorbed. Such a body is called absolutely black .

Bodies that
,
those. The whole thermal flow falling on the body is reflected from it, called white . At the same time, if the reflection from the surface is subject to the laws of body optics are called mirrored - if the diffuse reflection – absolutely white .

Bodies that
,
those. the whole thermal stream falling on the body passes through it, called diathermic or absolutely transparent .

There are no absolute bodies in nature, but the concept of such bodies is very useful, especially about absolutely black body, since the laws that control it by radiation are particularly simple, because no radiation is reflected from its surface.

In addition, the concept of absolutely black bodies makes it possible to prove that there are no such bodies in nature that emit more heat than black.

For example, in accordance with the Law of the Kirchhoff, the ratio of the emissivity of the body and its absorption capacity equally for all bodies and depends only on temperature, for all bodies, including absolutely black, at a given temperature:

(3)

Since the absorption capacity of absolutely black bodies
but and etc. Always less than 1, then from the Law of Kirchhoff it follows that the maximum radiative ability it has an absolutely black body. Since there are no absolutely black bodies in nature, the concept of gray body is introduced, its degree of black ε, which is the ratio of the radiative ability of gray and absolutely black bodies:

Following the law of Kirchhoff and considering that
can be recorded
from
those . The degree of black characterizes both the relative emissivity and the absorption capacity of the body . The main power of radiation reflecting the dependence of the radiation intensity
called to this range of wavelengths (monochromatic radiation) is the law of a plank.

(4)

where - wavelength, [m];

;

and - The first and second regular plank.

In fig. 1.2 This equation is represented graphically.

Fig. 1.2. Graphic Presentation of Plank Law

As can be seen from the graph, absolutely black body radiates at any temperature in a wide range of wavelengths. With increasing temperature, the maximum radiation intensity shifts towards shorter waves. This phenomenon is described by the Law of Wine:

Where
- The wavelength corresponding to the maximum of radiation intensity.

At values
instead of the Planck law, it is possible to apply the law of relay-jeans, which also wears the name "Long wavelength law":

(6)

The radiation intensity attributed to the entire wavelength interval from
before
(integral radiation), can be determined from the plan of the plan by integrating:

where - the radiation coefficient of absolutely black body. The expression is called the Staen-Boltzmann law, which was established by Boltzmann. For gray bodies, the law of Stefan-Boltzmanna is written in the form:

(8)

- Maudible gray body ability. The heat transfer is determined by the radiation between the two surfaces on the basis of the Stephen-Boltzmann law and has the form:

(9)

If a
, then the degree of blackness becomes equal to the degree of surface black .
. This circumstance is based on the method of determining the radiative ability and the degree of black bodies that have minor sizes compared to bodies that are exchanged with a radiant energy

(10)

(11)

As can be seen from the formula, determination of the degree of black and radiative ability FROMgray body need to know the surface temperature test Body, Temperature environment and radiant thermal stream from body surface
. Temperature and can be measured by known methods. And the radiant thermal stream is determined from the following considerations.

The propagation of heat from the surface of the bodies into the surrounding space is due to radiation and heat transfer at free convection. Full flow from the body surface, thus will be equal to:

From!
;

- Convective component of the heat flux, which can be determined by the law of Newton Richmana:

(12)

In turn, the heat transfer coefficient can be determined from the expression:

(13)

the decisive temperature in these expressions is the temperature of the borderline layer:

Fig. 2 Experimental Installation Scheme

Legend:

In - switch;

P1, P2 - voltage regulators;

PW1, PW2 - power meters (wattmeters);

NE1, NE2 - heating elements;

IT1, IT2 - temperature meters;

T1, T2, etc. - Thermocouples.

Federal Education Agency

State educational institution of higher

Vocational education

"Ivanovo State Energy University

Named after VI Lenin "

Department of theoretical foundations of heat engineering

Determination of the integral degree of solid black

Methodical instructions for laboratory work

Ivanovo 2006.

Compilers V.V. Bukhimirov

THOSE. Sozinov

Editor D.V. Racutina

Methodical instructions are designed for students studying in the specialties of the heat engineering profile 140101, 140103, 140104, 140106 and 220301 and studying the course "Heat and heat exchange" or "heat engineering".

Methodical instructions contain a description of the experimental installation, the methodology for conducting the experiment, as well as the calculated formulas necessary for processing the results of experience.

Methodical instructions approved by the Cycle Methodical Commission of the TEF.

Reviewer

department of Theoretical Fundamentals of Heat Engineering Ivanovo State Energy University

1. Task

1. Experimentally determine the integral degree of black thin tungsten thread.

2. Compare the results of the experiment with reference data.

2. Brief information from the theory of radiation heat exchange

Thermal radiation (radiation heat exchange) is a method of heat transfer in space, carried out as a result of the propagation of electromagnetic waves, the energy of which when interacting with the substance goes into heat. Radiation heat exchange is associated with a double energy conversion: Initially, the internal energy of the body turns into the energy of electromagnetic radiation, and then after transferring the energy in space-electromagnetic waves, the second transition of radiant energy occurs in the inner energetic body.

The thermal radiation of the substance depends on the body temperature (degree of heatedness of the substance).

The energy of thermal radiation falling on the body can be absorbed, reflect the body or pass through it. The body absorbing the whole inclusive energy falling on it, call an absolutely black body (ACT). Note that at this temperature of the ACT and radiates the maximum possible amount of energy.

The density of the stream of its own radiation of the body is called it lanesispeting ability. This radiation parameter within the elementary section of wavelengths is called spectral flow density of own radiation or spectral body diffusing body. The diffusing capacity of ACT, depending on the temperature, is subject to the law of Stephen Boltzmann:

, (1)

where  0 \u003d 5,67 €10 -8 W / (m 2 k 4) is the constant Stephen-Boltzmann; \u003d 5.67 W / (m 2 K 4) - the radiation coefficient of absolutely black body; T - The surface temperature of absolutely black body, K.

Absolutely black bodies in nature do not exist. The body whose radiation spectrum is similar to the emission spectrum of absolutely black body and the spectral density of the radiation stream (E ) is the same share   on the spectral density of the emission flux of absolutely black body (E 0, λ), called gray tel:

, (2)

where   is the spectral degree of black.

After integrating the expression (2) throughout the emission spectrum (
) We will get:

, (3)

where e is the scoring ability of the gray body; E 0 is the scattering ability of the ACT; - integral degree of black in the gray body.

From the last formula (3), taking into account the Stefan-Boltzmann's law, an expression should be an expression for calculating the density of the flow of eigen radiation (diffusing ability) of the gray body:

where
- the radiation coefficient of the gray body, W / (m 2 k 4); T - Temperature of the body, K.

The value of the integral degree of black depends on the physical properties of the body, its temperature and the surface roughness of the body. The integral degree of black is determined experimentally.

In the laboratory work, the integral degree of the black tungsten is found, exploring the radiation heat exchange between the heated tungsten thread (body 1) and the walls of the glass cylinder (body 2) filled with water (Fig. 1).

Fig. 1. Diagram of radiation heat exchange in the experiment:

1 - heated thread; 2 - the inner surface of the glass cylinder; 3 - Water

The resulting thermal stream obtained by a glass cylinder can be calculated by the formula:

, (6)

where  pr is the degree of black in the system of two bodies;  1 and  2 - integral degrees of the blackness of the first and second body; T 1 and T 2, F 1 IF 2 - absolute temperatures and surface areas of the heat exchange of the first and second body;  12 and 21 - angular radiation coefficients, which show which proportion of hemispherical radiation energy falls from one body to another.

Using the properties of angular coefficients is easy to show that
, but
. Substituting the values \u200b\u200bof the angular coefficients in formula (6), we get

. (7)

Since the surface area of \u200b\u200ba tungsten thread (body 1) is much less than the area of \u200b\u200bits surrounding shell (body 2), then the angular coefficient  21 tends to zero:

F 1 F 2
 21 \u003d F 1 / F 2 0 or
. (8)

Taking into account the latter withdrawal from formula (7), it follows that the reduced degree of black system of the two bodies depicted in Fig. 1 is determined only by the radiation properties of the surface of the thread:

 Pr 1 or
. (9)

In this case, the formula for calculating the resulting heat flux perceived by a glass cylinder with water takes the form:

it follows the expression to determine the integral degree of black tungsten thread:

, (11)

where
- Surface area Tungsten thread: Di - Diameter and thread length.

The radiation coefficient of tungsten threads is calculated according to the obvious formula:

. (12)

Planck law. The radiation intensity of the absolutely black body I Sl and any real body I l depend on the wavelength.

Absolutely black body with this eats the rays of all wavelengths il \u003d 0 to l \u003d ¥. If it is in some way to separate the rays with different wavelengths from each other and measure the energy of each beam, it turns out that the distribution of energy along the spectrum is different.

As the wavelength increases, the energy of the rays increases, at a certain length, the wave reaches the maximum, then decreases. In addition, for the beam of the same wavelength, its energy increases with an increase in the body emitting the rays (Fig. 11.1).

The planke has established the following law of changing the intensity of emission of absolutely black body depending on and wavelength:

I Sl \u003d C 1 L -5 / (E C / (L T) - 1), (11.5)

Substituting into equation (11.7) the law of the plank and integrating from from L \u003d 0 to L \u003d ¥, we find that the integral radiation (thermal flow) of an absolutely black body is directly proportional to the fourth degree of its absolute (Stephen-Boltzmann law).

E S \u003d C (T / 100) 4, (11.8)

where with S \u003d 5.67 W / (m 2 * K 4) - the radiation coefficient of absolutely black body

Noting in Fig. 11.1. The amount of energy corresponding to the luminous part of the spectrum (0.4-0.8 MK) is not difficult to notice that it is very small for low compared to the energy of integral radiation. Only at the Sun ~ 6000k, the energy of light rays is about 50% of the entire energy of black radiation.

All real bodies used in the technique are not absolutely black and at the same time emit less energy than absolutely black body. Radiation of real bodies also depends on the wavelength. In order for the laws of radiation of the black body can be applied to real bodies, the concept of body and radiation is introduced. Under the radiation, it is understood as such, which is similar to the radiation of the black body has a solid spectrum, but the intensity of the rays for each wavelength I l with any constitutes a constant share of the intensity of the emitting of the black body I Sl, i.e. There is a relation:

I L / I SL \u003d E \u003d const. (11.9)

The value of E is called the degree of black. It depends on the physical properties of the body. The degree of black bodies always less than one.

Kirchhoff law. For every body, radiative and absorption abilities depend on and wavelength. Various bodies have different meanings E and A. Dependence between them is established by the Circhoff law:

E \u003d E S * A or E / A \u003d E S \u003d E S / A S \u003d C S * (T / 100) 4. (11.11)

The ratio of the leisure ability of the body (E) to its rule of sparing ability (a) is equally for all bodies that are at the same and equal to the scattering ability of an absolutely black body with the same.

From the Law of Kirchhoff, it follows that if the body has a small absorption capacity, it simultaneously possesses both low leaning ability (polished). Absolutely black body, which has the maximum absorption capacity, has the greatest radiative ability.

The Law of Kirchhoga remains fair for monochromatic radiation. The ratio of the intensity of the radiation of the body at a certain wavelength to its absorption capacity at the same wavelength for all bodies is the same if they are with the same, and numerically equal to the intensity of the emission of absolutely black bodies at the same wavelength and, i.e. It is a function only wavelength and:

E L / a L \u003d i L / A L \u003d E Sl \u003d I Sl \u003d F (L, T). (11.12)

Therefore, the body that emits energy at some wavelength is capable of absorbing it at the same wavelength. If the body does not absorb energy into some part of the spectrum, then it does not radiate in this part of the spectrum.

From the law of Kirchhoff, it also follows that the degree of blackness of the body E with the same numerically equal to the absorption coefficient A:

e \u003d i L / I Sl \u003d E / E SL \u003d C / C SL \u003d A. (11.13)

Lambert law. Bulk radiated radiant energy spreads in space in various directions with different intensity. The law establishes the dependence of the radiation intensity from the direction is called the Lambert law.

Lambert law establishes that the amount of radiant energy emitted by the element of the DF 1 surface in the direction of the DF 2 element is proportional to the product of the amount of energy emitted according to the normal of DQ N, by the size of the spatial angle of DC and COST, composed of the radiation direction with the normal (Fig. 11.2):

d 2 Q n \u003d DQ N * DW * COSJ. (11.14)

Consequently, the greatest amount of radiant energy is emitted in the perpendicular direction to the radiation surface, i.e., at (j \u003d 0). With increasing J, the amount of radiant energy decreases and is zero at j \u003d 90 °. The Lambert law is fully fair for absolutely black bodies and for bodies with diffuse radiation at j \u003d 0 - 60 °.

For polished surfaces, Lambert law is not applicable. For them, radiating with j will be greater than in the direction, normal to the surface.