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To verify the Stefan’s law by Electrical method – Physics Practical

Stefan’s law states  that the energy radiated per second by unit area of a black body at thermodynamic  temperature T is directly proportional to T 4 . The constant of proportionality is the Stefan constant, equal to 5.670400 × 10 –8 Wm –2 K –4 . This practical will verify this law using electrical method.

Practical of verification of Stefan’s law

Watch this Video to know about Stefan’s Law

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Experiments on the Stefan-Boltzmann-law

Introduction: Experiments on the Stefan-Boltzmann-law

A body with a certain temperature T emits electromagnetic radiation. This is noticeable in a forge, for example, when the piece of iron is brought to a high temperature. The spectrum of that radiation was already known around 1900, but it was not possible to derive it theoretically satisfactorily.

Two existing theoretical approximations failed to fully describe the intensity curve of this thermal radiation. While the Rayleigh-Jeans law only agreed with the experimental results for large wavelengths (low frequencies) and predicted the so-called ultraviolet catastrophe for increasing frequencies, Wien's radiation law only predicted the correct intensity profile for small wavelengths (high frequencies).

The German physicist Max Planck devoted himself to this theoretical challenge of so-called black body radiation. He postulated that electromagnetic radiation can only be emitted in energy portions E = h · f = h · c / λ. This can be described as the birth of quantum physics. Under this assumption, he received an expected intensity profile which was in excellent agreement with the experimental results.

The formula he derived for the spectral intensity curve is attached.

M_0_λ (λ, T) is the radiation power that is emitted by the surface element dA in the wavelength range between λ and λ + dλ in the entire half-space. In addition to the wavelength λ, the intensity profile depends on the temperature T:

What can you tell from the above spectra? The higher the temperature T, the further the radiation maximum shifts to the left in the direction of the smaller wavelength. At a temperature of 5800 K, for example, the maximum radiation is at a wavelength of approx. 500 nm. This roughly corresponds to the intensity curve of our sun. Their surface temperature must therefore also be in this range. The simple relationship between λ_max and temperature T describes Wien’s law of displacement, which reads:

λ_max [in μm] = 2897.8 / T [in K]

However, it can also be seen that the area under the curve increases sharply with increasing temperature. The area under the intensity curve corresponds to the energy radiated over all wavelengths per second and square meter, i.e. the total radiation intensity.

The two Austrian physicists Josef Stefan and Ludwig Boltzmann found a simple relationship for this, which is:

I_ges = σ · T ^ 4 with σ = Stefan-Boltzmann constant = 5.67 · 10 ^ –8 W / m ^ 2 · K ^ 4

A body with twice the temperature therefore emits a total of 16 times the energy per second and m ^ 2.

Step 1: The Black Body Radiation Source

For the black body radiation source you need a common light bulb. I use a 12V/5W one.

If you know the voltage U and the current I through the light bulb, the resistance R = U / I of the tungsten filament can be calculated very easily. However, this resistance R depends on the temperature T of the filament. The formular for calculating the temperature T with a given resistance R/R_room_temperature is attached. It works for tungsten filaments. You just need to know the resistance R_room_temperature of the filament at room temperature (bulb without a current/voltage just connected to the Ohmmeter) and the resistance R at the calculated temperature T.

Parts you will need:

• a AC/DC power supply. I use a 14V/60W model, but you can take f.e. your old laptop-power-supply: power supply
• a 5A DC/DC step down converter: buck-converter ebay
• a 12V/5W bulb with E10 thread: bulb ebay
• a E10 lamp holder: lamp holder ebay
• a multiturn 50kohm-potentiometer: 50k potentiometer ebay
• a 4 digits digital panelmeter for voltage and current: panelmeter ebay

Step 2: The DIY Thermopile

The radiation-power emitted by the light bulb at temperature T is measured with a so-called thermopile. You can simply build your own thermopile using a peltier-element and some other parts like plastic-tubes, a heatsink and some resistors for calibrating your apparatus.

The power (energy per second) or intensity (energy per second and per m²) of thermal radiation can be determined with a thermopile. The heart of a thermopile is a so-called Peltier element. This is based on the so-called thermo-electric voltage. If you combine two pieces of wire from different metals and bring the two contact points to different temperatures, you measure a so-called thermal voltage. In the Peltier element, many such “pieces of wire” are arranged one behind the other and alternately in order to intensify the effect. If, for example, a laser is shone on a side of the Peltier element blackened with soot, its radiation is absorbed and this side heats up slightly. As a result, a likewise very small thermal voltage U can be measured on the two cables of the Peltier element. This is a measure of the absorbed radiant power P.

To determine the relationship U = U (P), several SMD resistors are glued in series on one side of the Peltier element. I used 10 pieces of 1 kohm SMD-resistors connected in parallel to get a total resistance of 100 ohms.

Then you apply a certain voltage to this series of resistors, calculate the electrically supplied power P and measure the thermal voltage U. In my case, I got the linear relationship U = (1 / 11.26) * P. A power of e.g. 20 mW generated a thermal voltage of 1,776 mV. Conversely, a voltage of 1 mV corresponds to a radiation power of 11.26 mW. This relationship is required to determine the radiated power P in the Arduino program.

The Peltier element has an area of 40 × 40 mm² = 1600 mm². In order to be able to deduce the radiation intensity (power per m²), the power applied to the Peltier element must simply be multiplied by the factor (1000000/1600) = 625. If, for example, the power impinging on the Peltier element is 5 mW, then exactly 5 * 625 = 3125 mW = 3,125 W would impinge on 1 m², which then corresponds to an intensity of 3,125 W / m².

Step 3: The Arduino-part

Since the output voltages of the thermopile are very low (in the µV-mV range), they are first amplified 10 times with an operational amplifier of the AD8551 type. You need an operational amplifier with a very low input offset voltage!

Then the amplified voltage goes to the ADS1115 AD converter module. Finally, the 16x2 display shows the thermal voltage (in mV), the total radiation power (in mW) and the radiation intensity per m² (= radiation power * 625; in W / m²).

The displayed values can be set to 0 with a button if a voltage/power/intensity WITHOUT radiation source is displayed (= offset).

Attachments

Step 4: the experiment.

In this experiment to verify the Stefan-Boltzmann-law, the radiation-power emitted by the light bulb at temperature T is measured with the thermopile. To do this, the light bulb is positioned a certain distance in front of the thermopile and then the light bulb voltage U is slowly increased. The radiant power P recorded by the thermopile is then measured as a function of the bulb voltage U. With the values for the voltage U and current I you can simply determine the resistance R of the tungsten filament. With the formular shown in step 1 you can calculate the temperature T.

Finally you draw a graph with the radiant-power P as a function of T^4 - T_room^4. If everything works perfect, you should get a straight line. This means, that the radiation-power emitted by a black body increases with the fourth power of the temperature as the Stefan-Boltzmann-law predicts.

Step 5: The Simpler Variant

If you don't have a thermopile for direct measurement of the radiant power emitted by the light bulb, you can instead simply plot the electrical power supplied to the light bulb P = U · I as a function of T^4 - T_room^4. Because in the case of equilibrium, the electrical power supplied to the light bulb must correspond to the emitted radiation power!

You should also get a straight line for the graph P = P(T^4 - T_room^4) as a proof of the Stefan-Boltzmann-law.

If you are interested in more physics experiments, take a look at my youtube-channel or my homepage:

my youtube-channel

my homepage

6.1 Blackbody Radiation

Learning objectives.

By the end of this section, you will be able to:

• Apply Wien’s and Stefan’s laws to analyze radiation emitted by a blackbody
• Explain Planck’s hypothesis of energy quanta

All bodies emit electromagnetic radiation over a range of wavelengths. In an earlier chapter, we learned that a cooler body radiates less energy than a warmer body. We also know by observation that when a body is heated and its temperature rises, the perceived wavelength of its emitted radiation changes from infrared to red, and then from red to orange, and so forth. As its temperature rises, the body glows with the colors corresponding to ever-smaller wavelengths of the electromagnetic spectrum. This is the underlying principle of the incandescent light bulb: A hot metal filament glows red, and when heating continues, its glow eventually covers the entire visible portion of the electromagnetic spectrum. The temperature ( T ) of the object that emits radiation, or the emitter , determines the wavelength at which the radiated energy is at its maximum. For example, the Sun, whose surface temperature is in the range between 5000 K and 6000 K, radiates most strongly in a range of wavelengths about 560 nm in the visible part of the electromagnetic spectrum. Your body, when at its normal temperature of about 300 K, radiates most strongly in the infrared part of the spectrum.

Radiation that is incident on an object is partially absorbed and partially reflected. At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it. Therefore, a good absorber of radiation (any object that absorbs radiation) is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a blackbody .

Although the blackbody is an idealization, because no physical object absorbs 100% of incident radiation, we can construct a close realization of a blackbody in the form of a small hole in the wall of a sealed enclosure known as a cavity radiator, as shown in Figure 6.2 . The inside walls of a cavity radiator are rough and blackened so that any radiation that enters through a tiny hole in the cavity wall becomes trapped inside the cavity. At thermodynamic equilibrium (at temperature T ), the cavity walls absorb exactly as much radiation as they emit. Furthermore, inside the cavity, the radiation entering the hole is balanced by the radiation leaving it. The emission spectrum of a blackbody can be obtained by analyzing the light radiating from the hole. Electromagnetic waves emitted by a blackbody are called blackbody radiation .

The intensity I ( λ , T ) I ( λ , T ) of blackbody radiation depends on the wavelength λ λ of the emitted radiation and on the temperature T of the blackbody ( Figure 6.3 ). The function I ( λ , T ) I ( λ , T ) is the power intensity that is radiated per unit wavelength; in other words, it is the power radiated per unit area of the hole in a cavity radiator per unit wavelength. According to this definition, I ( λ , T ) d λ I ( λ , T ) d λ is the power per unit area that is emitted in the wavelength interval from λ λ to λ + d λ . λ + d λ . The intensity distribution among wavelengths of radiation emitted by cavities was studied experimentally at the end of the nineteenth century. Generally, radiation emitted by materials only approximately follows the blackbody radiation curve ( Figure 6.4 ); however, spectra of common stars do follow the blackbody radiation curve very closely.

Two important laws summarize the experimental findings of blackbody radiation: Wien’s displacement law and Stefan’s law . Wien’s displacement law is illustrated in Figure 6.3 by the curve connecting the maxima on the intensity curves. In these curves, we see that the hotter the body, the shorter the wavelength corresponding to the emission peak in the radiation curve. Quantitatively, Wien’s law reads

where λ max λ max is the position of the maximum in the radiation curve. In other words, λ max λ max is the wavelength at which a blackbody radiates most strongly at a given temperature T . Note that in Equation 6.1 , the temperature is in kelvins. Wien’s displacement law allows us to estimate the temperatures of distant stars by measuring the wavelength of radiation they emit.

Example 6.1

Temperatures of distant stars.

When simplified, Equation 6.2 gives

Therefore, Betelgeuse is cooler than Rigel.

Significance

Check your understanding 6.1.

The flame of a peach-scented candle has a yellowish color and the flame of a Bunsen’s burner in a chemistry lab has a bluish color. Which flame has a higher temperature?

The second experimental relation is Stefan’s law , which concerns the total power of blackbody radiation emitted across the entire spectrum of wavelengths at a given temperature. In Figure 6.3 , this total power is represented by the area under the blackbody radiation curve for a given T . As the temperature of a blackbody increases, the total emitted power also increases. Quantitatively, Stefan’s law expresses this relation as

where A A is the surface area of a blackbody, T is its temperature (in kelvins), and σ σ is the Stefan–Boltzmann constant , σ = 5.670 × 10 −8 W / ( m 2 · K 4 ) . σ = 5.670 × 10 −8 W / ( m 2 · K 4 ) . Stefan’s law enables us to estimate how much energy a star is radiating by remotely measuring its temperature.

Example 6.2

Power radiated by stars.

The power emitted per unit area by a white dwarf is about 5000 times that the power emitted by a red giant. Denoting this ratio by a = 4.8 × 10 3 , a = 4.8 × 10 3 , Equation 6.5 gives

We see that the total power emitted by a white dwarf is a tiny fraction of the total power emitted by a red giant. Despite its relatively lower temperature, the overall power radiated by a red giant far exceeds that of the white dwarf because the red giant has a much larger surface area. To estimate the absolute value of the emitted power per unit area, we again use Stefan’s law. For the white dwarf, we obtain

The analogous result for the red giant is obtained by scaling the result for a white dwarf:

Check Your Understanding 6.2

An iron poker is being heated. As its temperature rises, the poker begins to glow—first dull red, then bright red, then orange, and then yellow. Use either the blackbody radiation curve or Wien’s law to explain these changes in the color of the glow.

Check Your Understanding 6.3

Suppose that two stars, α α and β , β , radiate exactly the same total power. If the radius of star α α is three times that of star β , β , what is the ratio of the surface temperatures of these stars? Which one is hotter?

The term “blackbody” was coined by Gustav R. Kirchhoff in 1862. The blackbody radiation curve was known experimentally, but its shape eluded physical explanation until the year 1900. The physical model of a blackbody at temperature T is that of the electromagnetic waves enclosed in a cavity (see Figure 6.2 ) and at thermodynamic equilibrium with the cavity walls. The waves can exchange energy with the walls. The objective here is to find the energy density distribution among various modes of vibration at various wavelengths (or frequencies). In other words, we want to know how much energy is carried by a single wavelength or a band of wavelengths. Once we know the energy distribution, we can use standard statistical methods (similar to those studied in a previous chapter) to obtain the blackbody radiation curve, Stefan’s law, and Wien’s displacement law. When the physical model is correct, the theoretical predictions should be the same as the experimental curves.

In a classical approach to the blackbody radiation problem, in which radiation is treated as waves (as you have studied in previous chapters), the modes of electromagnetic waves trapped in the cavity are in equilibrium and continually exchange their energies with the cavity walls. There is no physical reason why a wave should do otherwise: Any amount of energy can be exchanged, either by being transferred from the wave to the material in the wall or by being received by the wave from the material in the wall. This classical picture is the basis of the model developed by Lord Rayleigh and, independently, by Sir James Jeans. The result of this classical model for blackbody radiation curves is known as the Rayleigh–Jeans law . However, as shown in Figure 6.6 , the Rayleigh–Jeans law fails to correctly reproduce experimental results. In the limit of short wavelengths, the Rayleigh–Jeans law predicts infinite radiation intensity, which is inconsistent with the experimental results in which radiation intensity has finite values in the ultraviolet region of the spectrum. This divergence between the results of classical theory and experiments, which came to be called the ultraviolet catastrophe , shows how classical physics fails to explain the mechanism of blackbody radiation.

The blackbody radiation problem was solved in 1900 by Max Planck . Planck used the same idea as the Rayleigh–Jeans model in the sense that he treated the electromagnetic waves between the walls inside the cavity classically, and assumed that the radiation is in equilibrium with the cavity walls. The innovative idea that Planck introduced in his model is the assumption that the cavity radiation originates from atomic oscillations inside the cavity walls, and that these oscillations can have only discrete values of energy. Therefore, the radiation trapped inside the cavity walls can exchange energy with the walls only in discrete amounts. Planck’s hypothesis of discrete energy values, which he called quanta , assumes that the oscillators inside the cavity walls have quantized energies . This was a brand new idea that went beyond the classical physics of the nineteenth century because, as you learned in a previous chapter, in the classical picture, the energy of an oscillator can take on any continuous value. Planck assumed that the energy of an oscillator ( E n E n ) can have only discrete, or quantized, values:

In Equation 6.9 , f is the frequency of Planck’s oscillator. The natural number n that enumerates these discrete energies is called a quantum number . The physical constant h is called Planck’s constant :

Each discrete energy value corresponds to a quantum state of a Planck oscillator . Quantum states are enumerated by quantum numbers. For example, when Planck’s oscillator is in its first n = 1 n = 1 quantum state, its energy is E 1 = h f ; E 1 = h f ; when it is in the n = 2 n = 2 quantum state, its energy is E 2 = 2 h f ; E 2 = 2 h f ; when it is in the n = 3 n = 3 quantum state, E 3 = 3 h f ; E 3 = 3 h f ; and so on.

Note that Equation 6.9 shows that there are infinitely many quantum states, which can be represented as a sequence { hf , 2 hf , 3 hf ,…, ( n – 1) hf , nhf , ( n + 1) hf ,…}. Each two consecutive quantum states in this sequence are separated by an energy jump, Δ E = h f . Δ E = h f . An oscillator in the wall can receive energy from the radiation in the cavity (absorption), or it can give away energy to the radiation in the cavity (emission). The absorption process sends the oscillator to a higher quantum state, and the emission process sends the oscillator to a lower quantum state. Whichever way this exchange of energy goes, the smallest amount of energy that can be exchanged is hf . There is no upper limit to how much energy can be exchanged, but whatever is exchanged must be an integer multiple of hf . If the energy packet does not have this exact amount, it is neither absorbed nor emitted at the wall of the blackbody.

Planck’s Quantum Hypothesis

Planck’s hypothesis of energy quanta states that the amount of energy emitted by the oscillator is carried by the quantum of radiation, Δ E : Δ E :

Recall that the frequency of electromagnetic radiation is related to its wavelength and to the speed of light by the fundamental relation f λ = c . f λ = c . This means that we can express [link] equivalently in terms of wavelength λ . λ . When included in the computation of the energy density of a blackbody, Planck’s hypothesis gives the following theoretical expression for the power intensity of emitted radiation per unit wavelength:

where c is the speed of light in vacuum and k B k B is Boltzmann’s constant, k B = 1.380 × 10 −23 J/K . k B = 1.380 × 10 −23 J/K . The theoretical formula expressed in Equation 6.11 is called Planck’s blackbody radiation law . This law is in agreement with the experimental blackbody radiation curve (see Figure 6.7 ). In addition, Wien’s displacement law and Stefan’s law can both be derived from Equation 6.11 . To derive Wien’s displacement law, we use differential calculus to find the maximum of the radiation intensity curve I ( λ , T ) . I ( λ , T ) . To derive Stefan’s law and find the value of the Stefan–Boltzmann constant, we use integral calculus and integrate I ( λ , T ) I ( λ , T ) to find the total power radiated by a blackbody at one temperature in the entire spectrum of wavelengths from λ = 0 λ = 0 to λ = ∞ . λ = ∞ . This derivation is left as an exercise later in this chapter.

Example 6.3

Planck’s quantum oscillator, check your understanding 6.4.

A molecule is vibrating at a frequency of 5.0 × 10 14 Hz . 5.0 × 10 14 Hz . What is the smallest spacing between its vibrational energy levels?

Example 6.4

Quantum theory applied to a classical oscillator.

The energy quantum that corresponds to this frequency is

When vibrations have amplitude A = 0.10 m , A = 0.10 m , the energy of oscillations is

Check Your Understanding 6.5

Would the result in Example 6.4 be different if the mass were not 1.0 kg but a tiny mass of 1.0 µ g, and the amplitude of vibrations were 0.10 µ m?

When Planck first published his result, the hypothesis of energy quanta was not taken seriously by the physics community because it did not follow from any established physics theory at that time. It was perceived, even by Planck himself, as a useful mathematical trick that led to a good theoretical “fit” to the experimental curve. This perception was changed in 1905 when Einstein published his explanation of the photoelectric effect, in which he gave Planck’s energy quantum a new meaning: that of a particle of light.

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Determination of Stefan Boltzmann's Constant

To determine the value of Stefan Boltzmann's constant.

Specifications:

Hemispherical enclosure diameter - 200 mm

Size of water jacket for hemisphere- 260 mm

Base Plate, hylum diameter - 240 mm

Test disc diameter - 20 mm

Specific heat of test disc (Cp)- 0.4168 kJ/kg K

No. of thermocouples mounted of enclosure - 4

No. of thermocouples mounted on the disc- 1

No. of thermocouples mounted water heater - 1

Immersion water heating capacity - 2000 watts

Mass of test disc - 0.008 kg

Apparatus Required:

• Experimental setup for Stefan Boltzmann's constant determination, with heater arrangement.
• Stabilized power Supply
• Switch on the power supply and set an input voltage (65 V) using the Voltage regulator.
• Fill the Stainless Steel cubical vessel with 7 litres of water and heat the water to 80°C.
• Open the Values & allow the hot water to fill the chamber
• Allow the hot water to stabilize for 10 minutes & measure the temperature of the chamber and three different locations on the inner hemispherical surface.
• Measure temperature of test surface to evenly 10 secs until it reaches a steady state
• Calculate the Stefan Boltzmann's constant by applying Stefan Boltzmann’s law.

Observations:

Temperature of hot water T 1 = 80°C

Observation of disc temperature (T 5 ):

Formula Used

Emissive power (E) = σ A D T S 4

A D = Area of the disc ‘D’ in m 2

T S = Average surface temp of Enclosure = T 2 +T 3 +T 4 in K/3

The radiant energy of the disc D, emitting into the enclosure E D is

E D = σ A D T D 4 = σ A D (T avg 4 -T d 4 )

T D = Temperature of disc T 5 in K

The net energy transferred to the disc

m cp dT/dt= σ A D (T D 4 -T s 4 )

m - Mass rate of test disc in kg

Cp - Specific heat of test disc in kJ/kg K

Stefan Boltzmann's Constant (σ) = m C p (dT/dt)/A D (T D 4 -T s 4 ) W/m 2 K 4

Model graph :

Thus the Stefan Boltzmann's constant is determined as (σ) .............

Viva-Voce Questions

State stephan boltzmann law & its constant value.

The emissive power of a black body is proportional to fourth power of its absolute temperature & its constant’s value is 5.67x10-8 W/m2 K4

What is the effect on internal energy of an object during radiation?

In radiation, internal energy of an object decreases.

Define Emissive Power

It is defined as the total amount of radiation emitted by the body per unit time and unit area.

Define Monochromatic emissive Power

The energy emitted by the surface at a given length per unit time per unit area in all dimensions is known as monochromatic emissive power.

Define Radiation

The heat transfer from one body to another without any transmitting medium is known as radiation

Define Emissivity

It is defined as the ability of the surface of a body to radiate the heat.

What is meant by Gray body?

If a body absorbs a definite percentage of incident radiation irrespective of their wavelength, the body is known as Gray body.

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Heat Transfer Lab Lab Experiment list

• 1 Determination of Heat Transfer Coefficient Through Natural Convection
• 2 Determination of Heat Transfer Coefficient Through Forced Convection
• 3 Determination of Thermal Conductivity (Lagged Pipe)
• 4 Determination of Stefan Boltzmann's Constant
• 5 Determination of Thermal Conductivity (Insulating Powder)
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• 7 Determination of Effectiveness of a Heat Exchanger by Parallel Flow

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      log(f) = log(σ) + 4log(t) ,.

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2. Stefans Constant

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Stefan’s Law

Table of Contents

Josef Stefan was an Austrian physicist who made significant contributions to understanding blackbody radiation. In 1879, he formulated Stefan’s Law, which states that the radiant energy of a blackbody is proportional to the fourth power of its temperature. This means that a perfect blackbody, an object that absorbs all radiation falling on it, emits more energy as it gets hotter. Stefan’s Law was a crucial step in studying blackbody radiation and paved the way for the quantum theory of radiation.

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Stefan began his career as a lecturer in mathematical physics in 1858 and became a professor of physics in 1863. By 1866, he was the director of the Physical Institute at the University of Vienna. Five years later, he empirically derived Stefan’s Law , which was later theoretically confirmed by Ludwig Boltzmann. This combined work led to the law being named the Stefan-Boltzmann Law. Understanding “ What is Stefan’s Law ” helps us appreciate how energy emission changes with temperature.

Also Check: Wein’s Displacement Law

Stefan’s Law, also known as the Stefan-Boltzmann Law, explains the power radiated by a black body based on its temperature and surface area. Widely used in thermodynamics and astrophysics, Stefan’s Law helps us understand how objects like stars and planets emit radiation. Scientists use Stefan’s Law to study these celestial bodies and their behaviors. Additionally, Stefan’s Law has practical applications, such as in designing solar panels and other energy conversion devices. By applying Stefan’s Law, we can improve the efficiency of these technologies and gain deeper insights into the natural world.

What is Stefan’s Law?

Stefan’s Law, also known as the Stefan-Boltzmann Law , states that the total energy emitted per unit surface area of a black body across all wavelengths per unit of time is directly proportional to the fourth power of the black body’s thermodynamic temperature and its emissivity. In simpler terms, Stefan’s Law explains that the power emitted by a black body increases rapidly with its temperature. This law highlights that as the temperature of a black body rises, the amount of energy it emits also increases significantly. Stefan’s Law is crucial for understanding the relationship between temperature and radiation in black bodies.

Stefan-Boltzmann Constant

The Stefan-Boltzmann Constant, named after physicists Josef Stefan and Ludwig Boltzmann, is a key component in Stefan’s Law. This constant, symbolized by the Greek letter σ, serves as the proportionality factor in Stefan’s Law.

Also Check: Ohm’s Law

Value of the Stefan-Boltzmann Constant

In the SI unit system, the value of the Stefan-Boltzmann Constant is approximately 5.67 × 10 -8 watts per square meter per Kelvin to the fourth power (W/(m ² K ⁴ )). Here are its values in different unit systems:

• SI Units: 5.670367 × 10 -8 W/(m ² K ⁴ )
• CGS Units: 5.6704 × 10 5 erg/(cm ² s K ⁴ )
• Thermochemistry Units: 11.7 × 10 8 cal/(cm ² day K ⁴ )
• U.S. Customary Units: 1.714 × 10 9 BTU/(ft ² hr °R ⁴ )

The dimension of the Stefan-Boltzmann Constant is [M] 1 [L] 0 [T] -3 [K] -4 , representing mass (M), length (L), time (T), and temperature (K).

Understanding the Stefan-Boltzmann Constant is crucial for applying Stefan’s Law, which helps determine the radiant energy emitted by a blackbody based on its temperature.

Examples of Stefan’s Law

Welding is a process that joins two pieces of metal by heating them until they fuse together. During welding, sparks can be seen because energy is radiated into the surroundings. This demonstrates Stefan’s Law, which explains how energy is emitted as heat.

Calculating the Radius of Stars

The radius of a star can be calculated based on its luminosity, which is the total power radiated by the star into space. This power depends on the star’s surface area and temperature. Stefan’s Law shows the relationship between an object’s surface area, temperature, and the rate of radiation it emits, helping astronomers determine the size of stars.

Aluminium Foil

Aluminium foil is another example of Stefan’s Law in action. This law explains that objects with lower emissivity radiate less energy. Since aluminium foil has a low emissivity of about 0.1 units, it effectively keeps food warmer for longer periods by minimizing radiation loss.

These examples illustrate how Stefan’s Law applies to various real-world scenarios, from welding and astronomy to everyday uses like aluminium foil.

Also Check: Kirchoff’s Law

Understanding Stefan’s Law in Physics

Stefan’s Law , also known as the Stefan-Boltzmann Law, explains that the total radiant heat power emitted by a surface is proportional to the fourth power of its absolute temperature. The formula for Stefan’s Law is:

In this formula:

• E represents the radiant heat energy emitted per unit area per second.
• σ is the Stefan-Boltzmann constant.
• T is the absolute temperature.

Using Stefan’s Law, we can estimate the energy emitted by the Sun. Given the Sun’s photosphere temperature is around 6000 K, the energy emitted can be calculated as:

E sun ​=ϵσT 4

E sun ​=1×5.67×10 −8 ×(6000) 4

This results in an approximate energy emission of:

E sun ​≈25.12×10 9 J m −2 s −1

Stefan’s Law helps us understand the relationship between temperature and emitted radiation, providing insights into various physical phenomena.

Applications of Stefan-Boltzmann Law

Stefan’s Law, also known as the Stefan-Boltzmann Law , has many real-world applications. Here are a few important uses:

• Stefan’s Law helps scientists calculate the luminosity of celestial bodies such as stars, planets, and galaxies.
• The law is also used to understand how greenhouse gases affect our atmosphere. By using Stefan’s Law, scientists can calculate the amount of energy absorbed by the atmosphere and predict the impact of rising temperatures.
• Engineers apply Stefan’s Law to compare surface temperatures of different materials. This helps them design more power-efficient systems that do not require active cooling.

In these ways, Stefan’s Law plays a crucial role in astronomy, environmental science, and engineering.

Also Check: Charles Law

FAQs on Stefan’s Law

Who proposed stefan's law and when.

The Austrian physicist Josef Stefan proposed Stefan's Law in 1879.

Is the Stefan-Boltzmann law applicable to all bodies?

No, the Stefan-Boltzmann law is only applicable to black bodies, which are surfaces that can absorb all incident heat radiation.

What is the value of Stefan-Boltzmann’s constant?

In physics, the value of Stefan-Boltzmann’s constant is approximately 5.670374419 × 10−8 watts per meter² per Kelvin⁴.

How was the Stefan-Boltzmann constant discovered?

The Stefan-Boltzmann constant is named after Josef Stefan and Ludwig Boltzmann. Josef Stefan discovered this constant based on John Tyndall's 1864 measurements of infrared emissions from a platinum filament. In 1879, Stefan deduced the proportionality to the fourth power of absolute temperature from Tyndall’s work. Ludwig Boltzmann then derived the constant from theoretical principles in 1884, using the work of Adolfo Bartoli on radiation pressure and applying thermodynamics principles.

What is Stefan's Law?

Stefan's Law, or the Stefan-Boltzmann Law, states that the total energy emitted per unit time and per unit area of a blackbody is proportional to the fourth power of the blackbody's temperature.

How is the Stefan-Boltzmann constant derived?

One way to derive the Stefan-Boltzmann constant is by integrating Planck’s Radiation Formula.

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5 comments:

its helped me. thanx

How can we calculate T temperature

Would you mind to help me with the values please

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