# JAMES PRESCOTT JOULE (1818- 89)

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.

JAMES JOULE

Calorimeter used by Joule in his 1876 determination of the mechanical equivalent of 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 -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)

Manchester Museum of Science & Industry

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# WILLIAM THOMSON (known as LORD KELVIN) (1824-1907)

1848 – Scotland

‘Molecular motion (or heat) approaches zero at temperatures approaching -273.15 degrees C’

LORD KELVIN

This temperature is known as absolute zero. It is the theoretical lowest limit of temperature. Like the speed of light, absolute zero can be approached closely but cannot be reached; as to actually reach it an infinite amount of energy is required.

The temperature scale based on absolute zero is the kelvin scale (kelvin, symbol K without the degree sign). One kelvin degree equals one celsius degree.

The energy of a body at absolute zero is called ‘zero-point energy’. The twentieth century model states that atomic particles can exist only at certain energy levels; the lowest energy level is called the ground state and all higher levels are called excited states. At absolute zero all particles are in the ground state.

Thomson, together with JOULE, discovered the effect whereby most gases fall in temperature on expansion due to work taking place to pull apart the molecules. He independently enunciated and publicised the second law of thermodynamics describing the one-way spontaneous flow of heat – from a hotter body to a colder one. The German RUDOLPH CLAUSIUS also arrived at the same conclusion during the same period.

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# RUDOLPH CLAUSIUS (1822- 88)

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.

RUDOLPH CLAUSIUS

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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# 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’

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.

LUDWIG BOLTZMANN

## 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.)

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