1843 – England

‘A given amount of work produces a specific amount of heat’

4.18 joules of work is equivalent to one calorie of heat.

In 1798 COUNT RUMFORD suggested that mechanical work could be converted into heat. This idea was pursued by Joule who conducted thousands of experiments to determine how much heat could be obtained from a given amount of work.

Even in the nineteenth century, scientists did not fully understand the properties of heat. The common belief held that it was some form of transient fluid – retained and released by matter – called CALORIC. Gradually, the idea that it was another form of energy, expressed as the movement of molecules gained ground.
Heat is now regarded as a mode of transfer of energy – the transfer of energy by virtue of a temperature difference. Heat is the name of a process, not that of an entity.

Joule began his experiments by examining the relationship between electric current and resistance in the wire through which it passed, in terms of the amount of heat given off. This led to the formulation of Joule’s ideas in the 1840s, which mathematically determined the link.

Joule is remembered for his description of the conversion of electrical energy into heat; which states that the heat (Q) produced when an electric current (I) flows through a resistance (R) for a time (t) is given by Q=I2Rt

Its importance was that it undermined the concept of ‘caloric’ as it effectively determined that one form of energy was transforming itself into another – electrical energy to heat energy. Joule proved that heat could be produced from many different types of energy, including mechanical energy.

john collier portrait of james prescott joule


Joule's apparatus to show equivalence of work and heat

Joule’s apparatus to show equivalence of work and heat

Joule was the son of a brewer and all his experiments on the mechanical equivalent of heat depended upon his ability to measure extremely slight increases in temperature, using the sensitive thermometers available to him at the brewery. He formulated a value for the work required to produce a unit of heat. Performing an improved version of Count Rumford’s experiment, he used weights on a pulley to turn a paddle wheel immersed in water. The friction between the water and the paddle wheel caused the temperature of the water to rise slightly. The amount of work could be measured from the weights and the distance they fell, the heat produced could be measured by the rise in temperature.

Joule went on to study the role of heat and movement in gases and subsequently with WILLIAM THOMSON, who later became Lord Kelvin, described what became known as the ‘Joule-Thomson effect’ (1852-9). This demonstrated how most gases lose temperature on expansion due to work being done in pulling the molecules apart.

Thomson thought, as CARNOT had, that heat IN equals heat OUT during a steam engine’s cycle. Joule convinced him he was wrong.

The essential correctness of Carnot’s insight is that the work performed in a cycle divided by heat input depends only on the temperature of the source and that of the sink.

Synthesising Joule’s results with Carnot’s ideas, it became clear that a generic steam engine’s efficiency – work output divided by heat input – differed from one (100%) by an amount that could be expressed either as heat OUT at the sink divided by heat IN at the source, or alternatively as temperature of the sink divided by temperature of the source. Carnot’s insight that the efficiency of the engine depends on the temperature difference was correct. Temperature has to be measured using the right scale. The correct one had been hinted at by DALTON and GAY-LUSSAC’s experiments, in which true zero was minus 273degrees Celsius.

A perfect cyclical heat engine with a source at 100degrees Celsius and a sink at 7degrees has an efficiency of 1 – 280/373. The only way for the efficiency to equal 100% – for the machine to be a perfect transformer of heat into mechanical energy – is for the sink to be at absolute zero temperature.

Joule’s work helped in determining the first law of thermodynamics; the principle of the conservation of energy. This was a natural extension of his work on the ability of energy to transform from one type to another.

Joule contended that the natural world has a fixed amount of energy which is never added to nor destroyed, but which just changes form.

The SI unit of work and energy is named the joule (J).

link to James Joule - Manchester Museum of Science & Industry

Manchester Museum of Science & Industry

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BENJAMIN THOMPSON (1753-1814): known as Count Rumford

1798 – England

‘Mechanical work can be converted into heat. Heat is the energy of motion of particles’

Heat is a form of energy associated with the random motion of atoms or molecules. Temperature is a measure of the hotness of an object.

Portrait of COUNT RUMFORD ©


In the eighteenth century, scientists imagined heat as a flow of a fluid substance called ‘CALORIC‘. Each object contained a certain amount of caloric. If caloric flowed out, the object’s temperature decreased; if more caloric flowed into the object, its temperature increased.
Like phlogiston, caloric was a weightless fluid, a quality that could be transmitted from one substance to another, so that the first warmed the second up. What is being transmitted is heat energy.

One idea was that a hot object would emit ‘calorific rays’, whilst a cold one would emit ‘frigorific rays’ – an idea raised in Plutarch’s De Primo Frigido. Cold was an entity in itself, not simply the absence of heat.

It was believed that all substances contained caloric and that when a kettle was being heated over a fire, the fuel gave up its caloric to the flame, which passed it on to the metal, which passed it on to the water. Similarly, two pieces of wood rubbed together would give heat because abrasion was releasing caloric trapped within.

Working for the Elector of Bavaria, Rumford investigated the heat generated during the reaming out of the metal core when the bore of a cannon is formed. According to the caloric theory, the heat was released from the shards of metal during boring; Rumford noticed that if the tools were blunt and removed little or no metal, more heat was generated, rather than less. Rumford postulated that the heat source had to be the work done in drilling the hole. Heat was not an indestructible caloric fluid, as LAVOISIER had argued, but something that could come and go. Mechanical energy could produce heat and heat could lead to mechanical energy.

One analogy he drew was to a bell; heat was like sound, with cold being similar to low notes and hot, to high ones. Temperature was therefore just the frequency of the bell.

Rumford thought there was no separate caloric fluid and that the heat content of an object was associated with motion or internal vibrations – motion which in the case of the cannon was bolstered by the friction of the tools.
He had recognized the relationship between heat energy and the physicists’ concept of ‘work’ – the transfer of energy from a system into the surroundings, caused by the work done, results in a difference in temperature.
This transfer of energy measured as a temperature difference is called ‘heat’.

Half a century was to pass before in 1849, JAMES JOULE established the ‘mechanical equivalence of heat’ and JAMES CLERK MAXWELL launched the kinetic theory. According to Maxwell, the heat content of a body is equivalent to the sum of the individual energies of motion (kinetic energies) of its constituent atoms and molecules

US born Rumford founded the Royal Institution in London and invented the calorimeter, a device measuring heat.

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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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HANS BETHE (1906-2005)

1938 – USA

‘Energy in stars is produced by hydrogen fusion reactions’

In nuclear fusion the nuclei of light atoms combine at very high temperatures and release enormous amounts of energy that is radiated from the surface of the star as heat and light.

photo of HANS BETHE &copy:


An ordinary star is one of the simplest entities in nature; it is a sphere of gas that is by mass 73 percent hydrogen, 25 percent helium and 2 percent other elements. The temperature in the centre is high enough to fuse four nuclei of hydrogen together to form one helium nucleus.

picture of the Nobel medal - link to nobelprize.org

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