# JACQUES-ALEXANDRE-CESARE CHARLES (1746-1823)

1787 – France

‘The volume of a given mass of gas at constant pressure is directly proportional to its absolute temperature’

In other words, if you double the temperature of a gas, you double its volume. In equation form:  V/T = constant, or  V1/T1 = V2/T2,  where  V1 is the volume of the gas at a temperature  T1 (in kelvin) and  V2 the new volume at a new temperature  T2.

This principle is now known as Charles’ Law (although sometimes named after GAY-LUSSAC because of his popularisation of it fifteen years later – Gay Lussac’s experimental proof was more accurate than Charles’).
It completed the two ‘gas laws’.

A fixed amount of any gas expands equally at the same increments in temperature, as long as it is at constant pressure.

Likewise for a decline in temperature, all gases reduce in volume at a common rate, to the point at about minus 273degrees C, where they would theoretically converge to zero volume. It is for this reason that the kelvin temperature scale later fixed its zero degree value at this point.

CHARLES’ Law and BOYLE‘s Law may be expressed as a single equation, pV/T = constant. If we also include AVOGADRO‘s law, the relationship becomes pV/nT = constant, where n is the number of molecules or number of moles.

The constant in this equation is called the gas constant and is shown by R
The equation – known as the ideal gas equation – is usually written as pV = nRT

Strictly, it applies to ideal gases only. An ideal gas obeys all the assumptions of the kinetic theory of gases. There are no ideal gases in nature, but under certain conditions all real gases approach ideal behaviour.

# 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.

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.

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. 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.

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 equivalent 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.  TIMELINE HEAT

1824 – France

‘The Carnot cycle is the most efficient cycle for operating a reversible heat engine’

It illustrates the principle that the efficiency of a heat engine depends on the temperature range through which it works.

The cycle has a four-stage reversible sequence:

adiabatic compression and isothermal expansion at high temperature; adiabatic expansion and isothermal compression at low temperature.

( ADIABATIC: – no heat flows into or out of a system; ISOTHERMAL: – at a constant temperature )

Carnot suggested that the puissance motrice (motive power, by which he meant work or energy) of a heat engine was derived from the fall of heat from a higher to a lower temperature.

Carnot was the first to grasp the principles that later became known as the second law of thermodynamics.

By the time of Carnot’s death it had become clear there was no such thing as a calorific fluid ; heat is a form of energy, one of many, and the sum of all forms of energy in an isolated system is conserved. This has come to be known as the first law of thermodynamics.

In the case of a steam engine, the heat taken in at the boiler is not equal to the heat removed at the condenser. The work done by the ideal engine is the difference between the two. The first modern experiment proving the first law of thermodynamics was performed by a student of John Dalton’s, JAMES JOULE.  TIMELINE HEAT

# JULIUS ROBERT MAYER (1814- 78)

1842 – Germany

‘Heat is a form of energy and energy is conserved’

In equation form ΔE = H − W where ΔE is the change in the internal energy of a system, H is heat energy received by the system and W is work done by the system.

The first law of thermodynamics is simply a restatement of the law of the conservation of energy: energy is neither created nor destroyed, but may be changed from one form to another.

Mayer and HELMHOLTZ, independent of JOULE and each other, came to similar conclusions at around the same time.  TIMELINE HEAT

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

1848 – Scotland

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

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.  TIMELINE

# 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.

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.  TIMELINE