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

1879 – Austria

## STEFAN-BOLTZMANN CONSTANT

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

(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.

## BOLTZMANN CONSTANT

‘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. 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.)  TIMELINE HEAT