Stefan Boltzmann Constant

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]1 [T]-3 [Ꝋ]-4

Beside the SI unit, this can be expressed in various other systems of unit as well. Here, look at the table below for the same. 

SI. No. 

Unit type 

Unit of Stefan constant

Stefan constant value (σ)

1

Thermochemistry 

cal.cm2.day1.K4

11.7×108

2

CGS units 

erg.cm2.s1.K4

5.6704×105

3

US Customary Units 

BTU.hr1.ft2.°R4.

1.714×109


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. 

KB

Boltzmann constant 


h

Planck’s constant 

6.62607015 x 10-34 joule second

c

Speed of light 

3 x 108 m/S 

σ

Stefan Boltzmann’s constant 



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 R4) / (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. 

σ

Stefan Boltzmann’s constant


NA

Avogadro constant 

6.02214086 x 1023 mol-1

Universal gas constant

8.314 J/ (mol. K)

R

Rydberg Constant 

10973731.6 m-1

Ar(e)

Electron’s relative atomic mass 

1/ 1840

α

Structure constant

0.007297351

Mu

Molar mass constant

1 g / mol


Stefan Boltzmann constant – Uses and application

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. 

  1. q = α A T5

  2. q = α A T

  3. q = α A T3

  4. q = α A T4

Ans: d 

  1. Choose the appropriate unit for Stefan Boltzmann’s constant. 

  1. Kcal/hr K4

  2. Kcal/m2 hr K4

  3. Kcal/m2 K4

  4. Kcal/m hr K4

Ans: b 

You will be able to extend your learning about the Stefans constant and more with Vedantu’s study materials. Now you can also download our Vedantu app and easily learn the complex topics with the study notes prepared by our expert tutors. 

FAQ (Frequently Asked Questions)

1. What is the unit of Stefan’s constant?

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.

2. What is the black body?

A black body is considered as an ideal physical body which is capable of absorbing all electromagnetic radiation incident on it, irrespective of the angle of incidence or its frequency. 

3. What is Stefan’s law of black body radiation?

According to Stefan’s law of black body radiation, all the radiation emitting from a black body is proportionate to the fourth power of the absolute or thermodynamic temperature of the black body.