JOSEF STEFAN (1835- 93) LUDWIG BOLTZMANN (1844-1906)

1879 – Austria


‘The total energy radiated from a blackbody is proportional to the fourth power of the temperature of the body’

portrait drawing of JOSEPH STEFAN ©


(A blackbody is a hypothetical body that absorbs all the radiation falling on it)

Stefan discovered the law experimentally, but Boltzmann discovered it theoretically soon after.

photo portrait of LUDWIG BOLTZMANN &copy:



‘Heat at the molecular level’

Shortly after JAMES CLERK MAXWELL’s analysis of molecular motion, Ludwig Boltzmann gave a statistical interpretation of CLAUSIUS’s notion of entropy.

Coloured graphic depicting distribution of heat energy according to boltzman's model

Boltzmann’s formula for entropy is

S = k logW

 S  is entropy, k  is now known as Boltzmann’s constant and  W  is a measure of the number of states available to the system whose entropy is being measured.

The notion that heat flows from hot to cold could be phrased in terms of molecular motions. Molecules in a container collide with one another and the faster ones slow down while the slower ones speed up. Thus the hotter part becomes cooler and the colder part becomes hotter – thermal equilibrium is reached.

The Boltzmann constant is a physical constant relating energy at the individual particle level with temperature. It is the gas constant R  divided by the Avogadro constant NA :

k = R/NA 

It has the same dimension (energy divided by temperature) as entropy.

(In rolling a dice, a seven may be obtained by throwing a six and a one, a five and a two or a four and a three, while three needs only a two and a one. Seven has greater ‘entropy’ – more states.)

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1936 – Russia

‘In the Earth’s early atmosphere simple inorganic compounds combined to form complex organic compounds, which formed the first living cell’



Viewed correctly, life is compatible with the basic principles of physics and chemistry.

Life is possible, but entropy increases. The late nineteenth century way of looking at biological systems fits into this scheme – looking for patterns in large numbers – in assigning precise properties to classes and groups, not to individuals. At the beginning of the nineteenth century, an organism expended vital force in order to perform its work of synthesis and morphogenesis; at the end of the century, the belief was that it consumed energy.

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1850 – Germany

‘Heat does not flow spontaneously from a colder to a hotter body’

’The second law of thermodynamics’. The law says that many processes in nature are irreversible, never going backwards. It defines the direction of time (time cannot go backwards).

In 1857 Clausius wrote a paper entitled ‘The Kind of Motion We Call Heat’, relating average molecular motion to thermal quantities. Two years later, JAMES CLERK MAXWELL took up the problem using a statistical approach.

Clausius tried to understand why mechanical energy is in some sense a ‘higher’ form of energy than heat, and why it isn’t possible to change heat into mechanical energy with 100% efficiency, although the opposite is true.

He managed to link the degree of order and disorder in a system to the reversibility of a process.

ca. 1850s-1888 --- Original caption: Portrait of German mathematical physicist Rudolph Clausius (1822-1888), one of the founders of thermodynamics. Undated photograph. --- Image by © Bettmann/CORBIS ©


In 1865, Clausius used the term entropy as a measure of the disorder or randomness of a system. The more random and disordered a system is, the greater the entropy. The entropy of an irreversible system must increase; therefore, the entropy of the universe is increasing. A force acts to minimize the disequilibrium of energy and to maximize entropy, an object rolling down a hill can come to a stop by friction, but the heat generated through that friction cannot be used to bring the object back to the top.

  • First Law – The energy of the universe is constant

  • Second Law – The entropy of the universe tends to a maximum (overall disorder always increases)

  • The third law of thermodynamics, enunciated by Hermann Nernst (Nernst’s theorem) dictates that it is impossible to cool an object to a temperature of absolute zero ( -273.15 degrees Celsius ). Absolute zero temperature is a state of complete order.

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