MEASURING RADIATION INTENSITY OF OBJECTS

BLACK AS A FUNCTION OF TEMPERATURE (STEFAN-BOLTZMANN LAW)

Dwi Maryanti Putri*, Meili Yanti, Nurul Muthmainnah Herman

Laboratorium Fisika Modern Jurusan Fisika FMIPA

Universitas Negeri Makassar

Abstract. Experiments Measuring Radiation Intensity as a Function of Temperature dark matter (Stefan-

Boltzmann Law) aims to measure the intensity of radiation (relative) of a black body at a temperature range of

3000 C - 7000 C with a Moll thermopile and determine the relationship between the intensity of the radiation to

absolute temperature (Law Stefan- Boltzmann. Ekesperimen using an electric oven is equipped with accessories

black body would serve as 'an ideal black body'. the temperature sensor using a NiCr-Ni thermocouple connected

to a data logger to the computer Cassy. thermal radiation was measured using a thermopile Moll connected to

Cassy V box. the experimental results showed that the rate of the fourth power of the black body temperature

obtained using the analysis graph between log V (volts) with log T (kelvin) is |4.08 ± 2.62|the value is the value

of the rank of the temperature with accuracy levels of 55 , 1% and the ratio of cooling Newton's law constants (K

values) in theory, namely | -0.00015 ± 0.00004 | and the graph is | -0.000089 ± 0.00008 | with a degree of confidence

that is 91.5%. KEYWORDS: Radiation Black body , Temperature, Newton's Law of Cooling, Black Objects.

INTRODUCTION

Thermal (heat) from the sun to the earth

via electromagnetic waves. The move is called

radiation, which can take place in a vacuum.

Radiation emitted by an object as a result of

temperature is called heat radiation (thermal

radiation).

Each object continuously emit heat

radiation in the form of electromagnetic waves,

but generally things look to us because it

reflects the light that came to him, not because

he memacarkan heat radiation. New objects

appear as radiating heat if the temperature

exceeds 1000 K. Once the temperature of the

object to be improved, the relative intensity of

the spectrum of light it emits changes. This

causes a shift in the colors of the spectrum are

observed, which can be used to estimate the

temperature of an object.

Black body radiation is one of the great puzzle

of physics that triggered the revolution in

physics. This revolution gave birth to quantum

physics. Research on black body radiation

involves a lot of scientists.

There is no perfect black body. We can

only create objects that are closer to a black

body. although the surface of the box was

painted white Why is that? When radiation from

sunlight entering the pit box, the reflected

radiation repeatedly (several times) by the walls

of the box and after this reflection hamoir can

say no more radiation left over (all radiation has

been absorbed in the box) in other words, the

hole has been functioning absorbs all radiation

that came to him as a result of objects appear

black.

In the experiment "Intensity radisasi

determine the black body as a function of

temperature" aims to prove the experiments

conducted by the Max Planck Institute, which

filed hipotesisyang Planck contrary to the

classical theory of electromagnetic waves

which is the beginning of the birth of quantum

theory.

Quantum theory is very important in science

because, in principle, in theory could be used to

predict chemical properties and physics of a

substance [2]

In addition to determining the radiation

intensity, this lab also aims to teach the

scientific practitioner attitudes shown by

scientists conducting experiments in the past, so

that it can serve as an example and can be

applied in the process of this investigation.

The method used to determine the black body

radiation is by comparing the increase in

temperature of an object and its surface

properties, in which a black object absorbs heat

radiation at all wavelengths.

THEORI

Black body radiation is one of the great

puzzle of physics that triggered the revolution

in physics. This revolution gave birth to

quantum physics. Research on black body

radiation involves a lot of scientists. One of

them is Kirchhoff, a professor of physics at the

meeting Heidelberg.Kirchhoff found that the

spectral intensity, ie the intensity per unit

wavelength and per unit solid angle, from a

black body is a function of wavelength and

temperature but does not depend on the

dimensions of a black body the. In his writings,

Kirchhoff stresses the importance of finding the

form of the function.

The density of black body radiation

spectral intensity has a simple relation with the

spectral power density (energy per unit

wavelength per unit volume) of black body

radiation in the cavity. However, to prove it is

necessary to measure the intensity of the

spectral density, which unfortunately, at the

moment it can not be done. This measurement

can only be done 20 years kemudian.Waktu that

physicists can measure the intensity of the

whole spectrum without knowing that the

intensity of this spectrum depends on the

wavelength.

Josef Stefan (1835-1893) in Vienna in

1879 who first discovered that the meeting of

the entire spectrum of energy is proportional to

the fourth power of the temperature of a black

body.

Five years later, LudwigBoltzmann

(1844-1906) one of the leading pioneers of

statistical mechanics to introduce the concept of

radiation pressure, indicating that Stefan

empirical equation can be obtained theoretically

from the second law of thermodynamics.

Collaborative these two figures, Stefan and

Boltzmann, who started the first step in an effort

to discover the function of Kirchhoff. [4]

Kirchhoff (1859) shows the second law

of thermodynamics from that radias in bersifar

isotropic black body cavity, the radiation flux is

free from direction / orientation, then also are

homogeneous is equal to the radiation flux at

each point, and is the same in all the cavities at

a temperature the same for each wavelength.

Objects that absorb heat radiation at

wavelengths throughout the so-called black

body. Small hole in a hollow object behaves as

a perfect black body (this idea was first

proposed by Kirchhoff) [2]

Quantum theory began with the

phenomenon of black body radiation. When an

object is heated it will look emit radiation (eg

characterized by the emission of light colored).

Speaking of black body radiation means we talk

about objects that have the characteristics of a

perfect absorber of radiation that is about it. [3]

Principles Stefan-Boltzmann law states

that the total radiation emitted by an object is

proportional to the absolute temperature

increases the rank 4. Let the radiation emitted

from a surface is M (M = total radiated power),

then the amount of radiation emitted is defined

as,

4M T (1)

with σ = 5,67 ⋅10-8 W/m2K4 (Stefan-

Boltzmann constant).

At the same time a black body absorbs

radiation from the environment. So measuring

the M but M 'which radiation is absorbed from

the environment. Radiation emitted by the

environment as it is written,

4

o oM T (2)

Thus obtained,

4 4' oM T T (3)

An object that is not an ideal radiator also

satisfy the equation 3 her bag but has a

coefficient of absorption "e" whose value is less

than 1, so it is written:

4TeE (4)

Where, e = emissivity (0 ≤ e ≤ 1).

Radiation or light emission in solids show a

continuous spectrum as the heated gas. [2]

In 1894, Vienna with the idea that they

also generally show that the energy must be in

mathematical form as follows.

T

fgfTfu 3),( (5)

The above equation is the law of Wien. The

implications of this law are:

1. The distribution of black body radiation

spectrum for sembrang temperature can be

searched by the above formula.

2. When the function g(x) has a maximum

value for x> 0 then in force

T

bmaks (6)

Planck proposed that a vibrating athom and

memncarkan can only absorb energy again in

the form of bundles of energy called quanta. If

the energy quanta is proportional to the

frequency of the radiation, the energy will also

be great anyway, but because none of waves

that can have energy exceeds kT, then tidaka da

standing wave that quantum energy greater than

kT. This effectively limits the intensity of the

radiation. Planck formulation of the intensity of

radiation can be used to derive the law of Stefan

and Wien shift law, and in fact decrease Stefan

law of Planck's formula gives the Stefan-

Boltzmann constant relationship and tetpan

Planck [1]

EXPERIMENTAL METODHOLOGY

Every object radiates heat. The

intensity of heat radiation (electromagnetic

nature) increases with increasing temperature of

objects, as well as dependent on the nature of

the surface. At a particular wavelength, the

greater the heat radiation emitted, the greater the

heat radiation is absorbed by the object.

Objects that absorb heat radiation at

wavelengths throughout the so-called black

body. Small hole in a hollow object behaves as

a perfect black body (this idea was first

proposed by Kirchhoff). The tools and materials

in this experiment are:

1. A set of tools GmBH Leybold production

experiment, which consists of an electric

oven to 230 V voltage, Accessories black

object, Safety box with a ground connection,

Sensor Cassy, Cassy Lab, adapter NiCr-Ni,

NiCr-Ni temperature sensor 1.5 mm, box

μV, termofile Moll, a small optical bench,

shortrod, Buffer V-shaped, 28 cm,

Multiclamp Leybold, universal Clamp, and a

pair of 100 cm cable, red / blue.

2. Supplement: 1 PC with Windows 98

operating system or higher

3. Other equipment is recommended that

Satuimmersion pump 12 V, Satulow-voltage

power supply, One silicone tubing, 7 mm Ø,

and One laboratory bucket, 10 l.

Before observing the intensity of black

body radiation, we first learn all the components

that have been installed correctly so it does not

need to be setup again. After that we connect all

of the tools to a voltage source including a

computer that will be used in the data collection.

In this experiment, before turning on an

electric oven that has been fitted by a black

body accessory to first run the water pump for

approximately 2 minutes. After 2 minutes the

oven is turned on and wait until the temperature

rises 5000C oven, where the temperature

change is observed on the screen of computer

software that has been equipped with Cassy

Lab.

FIHURE 1. The series of experimental tools

Radiation Black Objects

In order Cassy enabled NiCr-Ni

temperature sensors and μV box and set the

temperature measurement range from 00C-

12000C and voltage of -3 mV - 3 mV.

Furthermore, observed changes in the intensity

of the radiation as a function of the temperature

at which we are going to wait for 1 hour or more

until the temperature reaches above 4000C.

when the temperature reaches 4000C started

recording measurement data by pressing the

symbol on the menu Cassy and stop recording

when you are at a temperature of 500C. it stores

data after the recording by clicking on the save

symbol on the menu Cassy.

FIGURE 2. Display Settings menu Cassy and

temperature sensors and voltage

EXPERIMENT RESULT AND DATA

ANALYSIS

After the observation of the values

obtained 400oC temperature produces a voltage

of 24.2 x 10-4 volts and when it is at a

temperature of 50 ° C produces a voltage of 2 x

10-6 volts, so from the above data shows that the

temperature of an object is directly proportional

to the voltage generated. The time required from

400oC to 50oC temperature is 7532 seconds.

The graph plots the results of the

relationship between voltage (log V) with

temperature (log T) to determine the value of

the fourth power of the temperature of the black

body is shown as a graph as follows.

FIGURE 3. Relationship between log V graph

and log T

Equation is linear in the graph log (T)

and log (V) is used for the radiation intensity

menganilisis relationship with the fourth power

of the temperature.

The analysis of the data:

I= 𝑒𝜎𝑇4

Note:

Eσ is a constant value, since the experiment

used is V, then::

V=T4

Log V= log T4

Log V= 4 log T

4=log𝑉

log𝑇

DK= R2 x 100%

KR= 100%-DK

∆p=R2m

PF= |𝑝 ± ∆𝑝|

Thus, the analysis of the graph

y = 4,7501x - 17,205 dan R² = 0,551

m= 4,7501

Note: the value of m = p, so:

The p-value = 4.7501 is the value that indicates

the rank of the absolute temperature as

equation shown in the intensity of black body

radiation Stefan-Boltzmann law.

The degree of confidence (DK) = R2 x 100%

= 55,1%

The relative error (KR) = 100% - DK = 44,9 %

Value Δp = R2 x p = 0.551 x 4.07501 = 2,62

Scientifically graph analysis results are reported

in two significant figures

𝑝 = |4.08 ± 2.62|

Figure 4. Graph of time relationship (s) on the

temperature (K)

The analysis of the data:

r=𝑟𝑜𝑒−𝑘𝑡

.𝑟

𝑟𝑜= 𝑒−𝑘𝑡

.ln𝑟

𝑟𝑜= −𝑘𝑡

y = 4,7501x - 17,205R² = 0,551

-6

-5

-4

-3

-2

-1

0

2,4 2,5 2,6 2,7 2,8 2,9

LOG

V (

v)

LOG T(O K)

y = 575,75200506e-0,00008996x

R² = 0,91499935

0

100

200

300

400

500

600

700

800

0 2000 4000 6000 8000

(SU

HU

(O

K)

WAKTU (S)

-k=𝑙𝑛

𝑟

𝑟𝑜

𝑡

k=−𝑙𝑛𝑟

𝑟𝑜

∆k=R2k

PF= |𝑘 ± ∆𝑘|

To analyze the cooling constants used Newton

equation of a line generated by a graph of time

and temperature. The equation of the line:

y = 575,75200506e-0,00008996x and R² =

0,91499935

then,

T = 575,75200506e-0,00008996x and R² =

0,91499935

Value of k = -0.00008996 s-1 is a constant

value that indicates cooling Newton.

The degree of confidence (DK) = R2 x 100%

= 91.5%

The relative error (KR) = 100% - DK

= 8.5%

Value Δk = R2 x k

= 0,91499935 x (-0,00008996)

= - 0.0000823 s-1

Scientifically graph analysis results are reported

in two significant figures

𝑘 = |−0.000089 ± 0,000082| s-1

The average value of Newton's constant

cooling obtained by using the equation

t

r

r

k

)ln(0 is equal to 0.00019.

Based on the above analysis can be

more pronounced if the temperature rank (p)

and the value of Newton's constant cooling of

the analysis presented in the following table.

Table 1. Comparison of Rank Value T In

Experiments With Reference Value

rank T

Reference 4

Experiment/plot

graph

𝑝 = |4.08 ± 2.62|

Table 2. Comparison of Cooling Newton's

Constant Value In Calculations With Garik Plot

Constant k (s-1)

Experiment/

plot graph

𝑘 = |−0.000089 ± 0,00008| s-1

Counting 0.00019 s-1

Based on the above analysis of the data

obtained by a graph of temperature to voltage,

overall it appears that the temperature is

proportional to the voltage. However, based on

the equation of the line formed by the graph of

the results obtained the rank of black body

temperature is |4.08 ± 2.62|. Value obtained

exceeds the value of the theory is 4. With a

55.1% degree of accuracy. The results differ

from theory due to the maximum temperature

used is not reached 5000C and the level of

sensitivity of NiCr-Ni temperature sensor. So

from the experimental results is said that the

temperature of the rank of four (T4) is directly

proportional to the voltage bersesuain the

Stefan-Boltzmann law.

Of the value equation of the line that is

contained in the graph, we can determine the

value of K to see that there is an exponential

equation of the line on the graph. Exponential

rank value on the graph is a plot of the value of

k is |−0.000089 ± 0,00008|𝑠−1 with a degree

of confidence that is 91.5%. When compared

with the value obtained by the calculation of the

value of k is |−0,00015 ± 0,00004|

CONCLUSION

The intensity of black body radiation

(represented by voltage) is proportional to the

temperature rise in rank 4 and those obtained

from experiments that |4.08 ± 2.62|. K values

obtained in theory or calculation |−0,00015 ±0,00004| and from the equation K values

obtained by |−0.000089 ± 0,00008|𝑠−1.

REFERENCE

[1].Kenneth Krane. 1992. Fisika Modern.

Terjemahan H. J. Wospakrik. Jakarta, Penerbit

Universitas Indonesia (UI-Press).

[2]. Malago, Jasruddin Daud. 2005. Pengantar

Fisika Modern. Badan Penerbit UNM.

Makassar.

[3]Serway, Raymond. J . 2010. Fisika untuk

Teknik dan Sains Edisi Keenam Buku Tiga.

Jakarta : Erlangga

[4].Subaer, dkk. 2014. Penuntun Praktikum

Eksperimen Fisika I Unit Laboratorium Fisika

Modern Jurusan Fisika FMIPA UNM.