How Does the Stefan Boltzmann Constant Impact Thermal Physics?
Josef Stefan and Ludwig Boltzmann together proposed the law of black body radiation. According to the law, the total heat radiation emitting from a black body is directly proportional to the fourth power of the thermodynamic or absolute temperature of the black body. The proportionality constant used for this equation was named Stefan Boltzmann constant and was expressed by the Greek symbol σ.
Value of Stefan Boltzmann Constant
Stefan’s constant was universally accepted, and its value was derived as
σ = 5.670367(13) × 10-8 W ⋅ m-2. K-4
From the above, the SI unit of Stefan’s constant can be written as W ⋅ m-2. K-4.
Here,
W stands for Watt.
m for Metre.
K for Kelvin.
Dimensional formula for Stefan Boltzmann law constant will be \[[M^1T^{-3}K^{-4}]\].
Beside the SI unit, Stefan Boltzmann Constant can be expressed in various other systems of the unit as well. Here, look at the table below for the same.
Formula for Stefan Boltzmann Constant Value
This value is derived using various other constants or evaluated experimentally as shown below:
σ = 2 . π5 KB4 / 15 h3 c2 = 5.670367(13) × 10-8 J . m-2. S-1 . K-4
Refer to the table mentioned below to know the physical quantities used in this equation.
According to CODATA, this Value of Stefan constant can be evaluated utilising this gas constant as mentioned below.
σ = 2π5 R4 / 15 h3 c2 NA4 = (32 π5 h R4 R∞4) / (15 Ar(e)4 Mu4 c6 α8)
Refer to the table mentioned below to know the physical quantities used in this equation and their values.
You need to give special attention to these tables as these are something that have more to do understanding before learning. You need to keep in mind that this part cannot be mugged up in any way. Therefore, your focus should be on gaining clarity of basic concepts. For this, Vedantu tutors hold your hand from initial to the end where you can attain clarity on simple to complex topics. Once you have gained knowledge on concepts, then you can move ahead towards uses and applications.
Stefan Boltzmann constant – Uses and Applications
There are several scenarios in Physics when this constant is used for determining various physical quantities and other constants. Here is a list of few applications –
This constant can be used for measuring the heat amount which a black body radiates.
This constant is handy for the conversion of units (Temperature K into intensity (W. m-2).
These are a few applications of Stefan constant value amongst several others. Knowing the value of this constant and how it is derived will help you in the calculation of several other physical quantities. Going further, answer the questions mentioned below and test your understanding of this topic.
Multiple Choice Questions
1.Choose the appropriate option which holds true for Stefan Boltzmann thermal radiation law.
q = α A T5
q = α A T
q = α A T3
q = α A T4
Ans: d
2.Choose the appropriate unit for Stefan Boltzmann’s constant.
Kcal/hr K4
Kcal/m2 hr K4
Kcal/m2 K4
Kcal/m hr K4
Ans: b
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1.What is the unit of Stefan’s constant?
Ans: The SI Unit of Stefan’s constant can be written as W ⋅ m-2. K-4. In CGS units, it can be expressed as erg.cm2.s1.K4, and in US customary units, it is BTU.hr1.ft2.°R4.
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FAQs on Stefan Boltzmann Constant Explained
1. What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law states that the total power (P) radiated per unit surface area of a perfect black body is directly proportional to the fourth power of its absolute temperature (T). The formula is expressed as P = σAT⁴, where 'A' is the surface area and 'σ' is the Stefan-Boltzmann constant.
2. What is the accepted value and symbol for the Stefan-Boltzmann constant?
The Stefan-Boltzmann constant is represented by the Greek letter sigma (σ). Its officially recognised CODATA value is approximately 5.670374 × 10⁻⁸ Watts per square metre per Kelvin to the fourth power (W·m⁻²·K⁻⁴).
3. What are the SI unit and dimensional formula for the Stefan-Boltzmann constant?
The Stefan-Boltzmann constant (σ) has specific units and dimensions that are crucial for calculations in physics.
- SI Unit: The standard unit is Watts per square metre per Kelvin to the fourth power, written as W·m⁻²·K⁻⁴.
- Dimensional Formula: The dimensional formula is [M¹ L⁰ T⁻³ K⁻⁴], where M represents mass, T represents time, and K represents temperature.
4. How is the Stefan-Boltzmann constant used in real-world applications?
The Stefan-Boltzmann constant is not just a theoretical value; it is essential for many practical applications, including:
- Astrophysics: It is used to estimate the surface temperature of stars by measuring the energy they radiate.
- Thermal Engineering: Engineers use it to design furnaces, engines, and heat exchangers, calculating heat loss and transfer efficiency.
- Climate Science: The law helps model the Earth's energy balance, understanding how much energy is radiated back into space.
- Thermography: Thermal imaging cameras use this principle to determine the temperature of objects by detecting their infrared radiation.
5. Why must temperature be in Kelvin for the Stefan-Boltzmann law, not Celsius?
The Stefan-Boltzmann law is based on absolute temperature, where zero signifies the complete absence of thermal energy. The Kelvin scale is an absolute scale (0 K is absolute zero). The T⁴ relationship in the law is a direct proportionality that only holds true on such a scale. Using Celsius, which is a relative scale where 0°C is just the freezing point of water, would produce incorrect results and make no physical sense, as a body at 0°C still radiates heat.
6. How does the Stefan-Boltzmann law apply to objects that are not perfect black bodies?
Real-world objects are not perfect black bodies; they are often called 'grey bodies'. For these objects, the Stefan-Boltzmann law is modified by introducing a factor called emissivity (ε). The formula becomes P = εσAT⁴. Emissivity is a dimensionless value between 0 and 1, representing how effectively an object radiates energy compared to a perfect black body (where ε = 1). A shiny, reflective object has a very low emissivity.
7. How is the value of the Stefan-Boltzmann constant derived from other fundamental constants?
The Stefan-Boltzmann constant (σ) is not just an experimentally measured value; it can be derived from other universal constants in physics. It is fundamentally linked to Planck's theory of black-body radiation. The derivation shows its value is given by the formula: σ = (2π⁵k⁴) / (15c²h³), where:
- k is the Boltzmann constant
- c is the speed of light in a vacuum
- h is Planck's constant
8. What is the fundamental physical relationship that the Stefan-Boltzmann constant describes?
The Stefan-Boltzmann constant serves as the fundamental bridge connecting an object's temperature (a microscopic property related to the kinetic energy of its particles) to the total radiant energy it emits (a macroscopic property). In essence, it quantifies exactly how much electromagnetic power a surface radiates simply because of its temperature, providing a crucial link between thermodynamics and electromagnetism.
