DANIEL BERNOULLI (1700- 82) JAMES CLERK MAXWELL (1831- 79)

1738 – Switzerland
1859 – England

‘Gases are composed of molecules which are in constant random motion and their properties depend upon this motion’

The volume of a gas is simply the space through which molecules are free to move. Collisions of the molecules with each other and the walls of a container are perfectly elastic, resulting in no decrease in kinetic energy. The average kinetic energy of a gas increases with an increase in temperature and decreases with a decrease in temperature. The theory has been extended to provide a model for two states of matter – liquids and solids.

Bernoulli had a great advantage over DEMOCRITUS. He knew that free atoms were more than simply tiny grains flying though space; they were tiny grains flying through space and obeying NEWTON’s Laws of Motion.
Bernoulli proposed a ‘bombardment theory’, which stated that a gas consisted of tiny particles in rapid, random motion like a swarm of angry bees. He realized that in the case of such a gas visualized as a host of tiny grains in perpetual frenzied motion, the atoms hammering relentlessly on the walls of any containing vessel would produce a force by bombarding the container. The effect of each individual impact would of course be vanishingly small. The effect of billions upon billions of atoms, hammering away incessantly, however, would be to push the walls back. A gas made of atoms would exert a jittery force that we would detect as a ‘pressure’.

Heating a gas would make its particles move faster.
The pressure of a gas such as steam was easy to measure using a piston in a hollow container. This was essentially a moveable wall. To deduce how the pressure of a gas would be affected by different conditions, Bernoulli first made some simplifying assumptions. He assumed the atoms were very small compared to the gulf between them. This allowed Bernoulli to ignore any force – whether of attraction or repulsion – that existed between them, as being unlikely to be ‘long range’. (This is an ‘ideal’ or ‘perfect’ gas. The behaviour of a real gas may differ from the ideal, for example at very high pressure). With the motion of each atom unaffected by its fellows, Newton’s laws dictated that it should fly at a constant speed in a straight line. The exception was when it slammed into a piston or the walls of the container. Bernoulli assumed that in such a collision a gas atom bounced off the walls of the surface without losing any speed, in the process imparting a miniscule force to the wall.

What would happen if the volume of the gas were reduced by applying an outside force to the piston? If the gas were reduced to half its original volume, the atoms would now have to fly only half as far between collisions, in any given time they would collide with the piston twice as many times and would exert twice the pressure. Similarly, if the gas were compressed to a third of its volume, its pressure would triple. This had been observed by ROBERT BOYLE in 1660 and named Boyle’s Law.

What would happen to the pressure of gas in a closed cylinder if the gas were heated while its volume remained unchanged? Exploiting the insight that the temperature of a gas was a measure of how fast on average its atoms were flying about, that when a gas was heated, its atoms speeded up, he deduced that as the atoms would be moving faster they would collide with the piston more often and create a greater force. Consequently the pressure of the gas would rise. This was observed by the French scientist JACQUES ALEXANDRE CESARE CHARLES in 1787, and christened Charles’ law.

After 120 years MAXWELL polished Bernoulli’s ideas into a rigorous mathematical theory. In Germany, LUDWIG  BOLTZMANN championed the atomic hypothesis, but was refuted by the Austrian ERNST MACH, who was convinced that science should not concern itself with any feature of the world that could not be observed directly with the senses.

BERNOULLI’S PRINCIPLE

‘As the velocity of a liquid or gas increases, its pressure decreases; and when the velocity decreases, its pressure increases’

At a narrow constriction in a pipe or tube, the speed of a gas or liquid is increased, but its pressure is decreased, according to Bernoulli’s principle. This effect is named the Venturi effect (and a pipe or tube with a narrow constriction the Venturi tube) after the Italian G.B. Venturi (1746-1822) who first observed it in constrictions in water channels. An atomiser works on the same principle.

 

The principle is expressed as a complex equation, but it can be summed up simply as the faster the flow the lower the pressure.

An aircraft wing’s curved upper surface is longer than the lower one, which ensures that air has to travel further and so faster over the top than it does below the wing. Hence the air pressure underneath is greater than on top of the wing, causing an upward force, called lift.

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LEONHARD EULER (1707- 83)

1755 – Switzerland

‘Analytical calculus – the study of infinite processes and their limits’

Swiss mathematician. His notation is even more far-reaching than that of LEIBNIZ and much of the mathematical notation that is in use to-day may be credited to Euler.

The number of theorems, equations and formulae named after him is enormous.
Euler made important discoveries in the analytic geometry of surfaces and the theory of differential equations.

Euler popularised the use of the symbols  Π (Pi);  e , for the base of the natural logarithm; and  i , for the imaginary unit.
Euler is credited with contributing the useful notations   f (x) , for the general function of  x ; and   Σ , to indicate a general sum of terms.

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HENRY CAVENDISH (1731-1810)

1766 – England

‘Three Papers Containing Experiments On Factitious Airs’

(gases made from reactions between liquids and solids)

1798 – Density of the earth
Using a torsion balance and the application of NEWTON’s theory of gravity, Cavendish concluded that the earth’s density was 5.5 times that of water.

Born of the English aristocracy and inheritor of a huge sum of money half way through his life, Cavendish is remembered for his work in chemistry.
He demonstrated that hydrogen (inflammable air) and carbon dioxide (fixed air) were gases distinct from ‘atmospheric air’. His claim to the discovery that water was not a distinct element – a view held since the time of ARISTOTLE – but a compound made from two parts hydrogen to one part oxygen, became confused with similar observations made by ANTOINE LAVOISIER.

Full length drawing of Henry Cavendish  &copy:

CAVENDISH

1871 – England

Almost all his discoveries remained unpublished until the late nineteenth century when his notes were found and JAMES CLERK MAXWELL dedicated himself to publishing Cavendish’s work, a task he completed in 1879.
By then many potential breakthroughs, significant at the time, had been surpassed by history.

In 1871 the endowment of the Cavendish Laboratory was made to Cambridge University by Cavendish’s legatees.

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HANS CHRISTIAN OERSTED (1777-1851)

1820 – Denmark

‘Electric current produces a magnetic field’

drawn portrait of HANS CHRISTIAN OERSTED ©

Oersted discovered that an electric current could make the needle of a magnetic compass swivel. It was the first indication of a link between these two natural forces. Although Oersted discovered electromagnetism he did little about it. This task was left to AMPERE and FARADAY.

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MICHAEL FARADAY (1791-1869)

1831 – England

‘A changing magnetic field around a conductor produces an electric current in the conductor. The size of the voltage is proportional to the rate of change of the magnetic field’

portrait drawing of MICHAEL FARADAY English chemist and physicist (British Library) (1791-1867)

This phenomenon is called ‘electromagnetic induction’ and the current produced ‘induced current’. Induction is the basis of the electric generator and motor.

Faraday developed HANS CHRISTIAN OERSTED’s 1820 discovery that electric current could deflect a compass needle. In his experiment Faraday wrapped two coils of insulated wire around opposite sides of an iron ring. One coil was connected to a battery, the other to a wire under which lay a magnetic compass needle. He anticipated that if he passed a current through the first wire it would establish a field in the ring that would induce a current in the second wire. He observed no effect when the current was steady but when he turned the current on and off he noticed the needle moving. He surmised that whenever the current in the first coil changed, current was induced in the second. To test this concept he slipped a magnet in and out of a coil of wire. While the magnet was moving the compass needle registered a current, as he pushed it in it moved one way, as he pulled it out the needle moved in the opposite direction. This was the first production of electricity by non-chemical means.

In 1831, by rotating a copper disc between the poles of a magnet, Faraday was able to produce a steady electric current. This was the world’s first dynamo.

NEWTON, with his concept of gravity, had introduced the idea of an invisible force that exerted its effect through empty space, but the idea of ‘action-at-a-distance’ was rejected by an increasing number of scientists in the early nineteenth century. By 1830, THOMAS YOUNG and AUGUSTIN FRESNEL had shown that light did not travel as particles, as Newton had said, but as waves or vibrations. But if this was so, what was vibrating? To answer this, scientists came up with the idea of a weightless matter, or ‘aether’.

Faraday had rejected the concept of electricity as a ‘fluid’ and instead visualised its ‘fields’ with lines of force at their edges – the lines of force demonstrated by the pattern of iron fillings around a magnet. This meant that action at a distance simply did not happen, but things moved only when they encountered these lines of force. He believed that magnetism was also induced by fields of force and that it could interrelate with electricity because the respective fields cut across each other. Proving this to be true by producing an electric current via magnetism, Faraday had demonstrated electromagnetic induction.

When Faraday was discovering electromagnetic induction he did so in the guise of a natural philosopher. Physics, as a branch of science, was yet to be given a name.

The Russian physicist HEINRICH LENZ (1804- 65) extended Faraday’s work when in 1833 he suggested that ‘the changing magnetic field surrounding a conductor gives rise to an electric current whose own magnetic field tends to oppose it.’ This is now known as Lenz’s law. This law is in fact LE CHATELIER‘s principle when applied to the interactions of currents and magnetic fields.

Fluctuating_Electromagnetic_Fields_and_EM_Waves

Fluctuating Electromagnetic Fields and EM Waves

It took a Scottish mathematician by the name of JAMES CLERK MAXWELL to provide a mathematical interpretation of Faraday’s work on electromagnetism.

Describing the complex interplay of electric and magnetic fields, he was able to conclude mathematically that electromagnetic waves move at the speed of light and that light is just one form of electromagnetic wave.
This led to the understanding of light and radiant heat as moving variations in electromagnetic fields. These moving fields have become known collectively as radiation.

Faraday continued to investigate the idea that the natural forces of electricity, magnetism, light and even gravity are somehow ‘united’, and to develop the idea of fields of force. He focused on how light and gravity relate to electromagnetism.
After conducting experiments using transparent substances, he tried a piece of heavy lead glass, which led to the discovery of the ‘Faraday Effect’ in 1845 and proved that polarised light may be affected by a magnet. This opened the way for enquiries into the complete spectrum of electromagnetic radiation.

In 1888 the German physicist HEINRICH HERTZ confirmed the existence of electromagnetic waves – in this case radio waves – traveling at the speed of light.

The unit of capacitance, farad (F) is named in honour of Faraday.

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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.

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 ©

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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JAMES CLERK MAXWELL (1831- 79)

1864 Scotland

‘Four equations that express mathematically the way electric or magnetic fields behave’

The Scottish physicist examined Faraday’s ideas concerning the link between electricity and magnetism interpreted in terms of fields of force and saw that they were alternative expressions of the same phenomena. Maxwell took the experimental discoveries of Faraday in the field of electromagnetism and provided his unified mathematical explanation, which outlined the relationship between magnetic and electric fields. He then proved this by producing intersecting magnetic and electric waves from a straightforward oscillating electric current.

In 1831 – following the demonstration by HANS CHRISTIAN OERSTED that passing an electric current through a wire produced a magnetic field around the wire, thereby causing a nearby compass needle to be deflected from north – MICHAEL FARADAY had shown that when a wire moves within the field of a magnet, it causes an electric current to flow along the wire.
This is known as electromagnetic induction.

In 1864 Maxwell published his ‘Dynamical Theory of the Electric Field’, which offered a unifying, mathematical explanation for electromagnetism.

In 1873 he published ‘Treatise on Electricity and Magnetism’.

The equations are complex, but in general terms they describe:

  • a general relationship between electric field and electric charge
  • a general relationship between magnetic field and magnetic poles
  • how a changing magnetic field produces electric current
  • how an electric current or a changing electric field produces a magnetic field

The equations predict the existence of electromagnetic waves, which travel at the speed of light and consist of electric and magnetic fields vibrating in harmony in directions at right angles to each other. The equations also show that light is related to electricity and magnetism.

Maxwell worked out that the speed of these waves would be similar to the speed of light and concluded, as Faraday had hinted, that normal visible light was a form of electromagnetic radiation. He argued that infrared and ultraviolet light were also forms of electromagnetic radiation, and predicted the existence of other types of wave – outside the ranges known at that time – which would be similarly explainable.

Verification came with the discovery of radio waves in 1888 by HEINRICH RUDOLPH HERTZ. Further confirmation of Maxwell’s theory followed with the discovery of X-rays in 1895.

photo portrait of JAMES CLERK MAXWELL ©

JAMES CLERK MAXWELL

Maxwell undertook important work in thermodynamics. Building on the idea proposed by JAMES JOULE, that heat is a consequence of the movement of molecules in a gas, Maxwell suggested that the speed of these particles would vary greatly due to their collisions with other molecules.

In 1855 as an undergraduate at Cambridge, Maxwell had shown that the rings of Saturn could not be either liquid or solid. Their stability meant that they were made up of many small particles interacting with one another.

In 1859 Maxwell applied this statistical reasoning to the general analysis of molecules in a gas. He produced a statistical model based on the probable distribution of molecules at any given moment, now known as the Maxwell-Boltzmann kinetic theory of gases.
He asked what sort of motion you would expect the molecules to have as they moved around inside their container, colliding with one another and the walls. A reasonably sized vessel, under normal pressure and temperature, contains billions and billions of molecules. Maxwell said the speed of any single molecule is always changing because it is colliding all the time with other molecules. Thus the meaningful quantities are molecular average speed and the distribution about the average. Considering a vessel containing several different types of gas, Maxwell realized there is a sharp peak in the plot of the number of molecules versus their speeds. That is, most of the molecules have speeds within a small range of some particular value. The average value of the speed varies from one kind of molecule to another, but the average value of the kinetic energy, one half the molecular mass times the square of the speed, (1/2 mv2), is almost exactly the same for all molecules. Temperature is also the same for all gases in a vessel in thermal equilibrium. Assuming that temperature is a measure of the average kinetic energy of the molecules, then absolute zero is absolute rest for all molecules.

The Joule-Thomson effect, in which a gas under high pressure cools its surroundings by escaping through a nozzle into a lower pressure environment, is caused by the expanding gas doing work and losing energy, thereby lowering its temperature and drawing heat from its immediate neighbourhood. By contrast, during expansion into an adjacent vacuüm, no energy is lost and temperature is unchanged.

The explanation that heat in gas is the movement of molecules dispensed with the idea of the CALORIC  fluid theory of heat.

The first law of thermodynamics states that the heat in a container is the sum of all the molecular kinetic energies.
Thermal energy is another way of describing motion energy, a summing of the very small mechanical kinetic energies of a very large number of molecules; energy neither appears nor disappears.
According to BOYLE’s, CHARLES’s and GAY-LUSSAC’s laws, molecules beating against the container walls cause pressure; the higher the temperature, the faster they move and the greater the pressure. This also explains Gay-Lussac’s experiment. Removing the divider separating half a container full of gas from the other, evacuated half allows the molecules to spread over the whole container, but their average speed does not change. The temperature remains the same because temperature is the average molecular kinetic energy, not the concentration of caloric fluid.

In 1871 Maxwell became the first Professor of Physics at the Cavendish Laboratory. He died at age 48.

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