Barometer
Evangelisto
Torricelli (1608-1647)
Torricelli (see photo) served as Galileo's secretary
(1641-1642) and succeeded him as court mathematician to Grand Duke Ferdinando
II. Torricelli used mercury to make the first barometer in 1643.
Mercury is more than 13 times as dense as water; a water barometer would
require a tube more than 30 feet long. Under standard conditions
at sea level, the height will be 29.92 inch or 760 millimeters. The invention
of the barometer allowed Boyle to discover the relationship between
pressure and volume.
(Torricelli letter
to Michelangelo concerning the Barometer).
Boyle's Law: P1V1=P2V2
Robert
Boyle (1627-1691)
Boyle (see photo) had the good fortune to have
Robert
Hooke as an assistant and together they made an air pump. Recognizing
its scientific possibilities, Boyle conducted pioneering experiments in
studying the role of air in combustion, respiration, and the transmission
of sound. In 1662, Boyle published what is now known as Boyle's law:
At constant temperature the volume of a gas is inversely proportional to
the pressure. Boyle was aware that a gas expands when heated but no temperature
scale existed and he could not determine the relationship between "hotness"
and volume.
Amontons' Law: P1T2=P2T1
Guillaume
Amontons (1663-1705)
Amontons developed the air thermometer--it relies on increase in volume
of a gas with temperature rather than the increase in volume of a
liquid. Amontons failed to discover Charles' law for the same reason
as Boyle: a temperature scale did not exist. Using the air
thermometer Amontons (1702) devised a method to measure change in temperature
in terms of a proportional change in pressure. Although Amontons' law became
the most obscure of the gas laws, it was this work that eventually
led to the concept of absolute zero in the 19th century.
As a consequence of becoming deaf as a young boy, Amontons worked on
inventions to benefit the deaf. One of his inventions, the
first
telegraph, relied on a telescope, light, and several stations
to transmit information over large distances. Although not adopted
in Amontons lifetime, the ideas were later refined and put into use.
Kinetic Theory of Gases
Daniel
Bernoulli (1700-1782)
Bernoulli (see photo) studied medicine at
the insistence of his father Johann Bernoulli, chair of mathematics in
Basel Switzerland. However the younger bernoulli became interested
in his father's theories of kinetic energy and even applied these theories
to his doctoral dissertation on the mechanics of breathing. While
practicing medicine in Venice, Bernoulli published his first mathematical
work consisting of four separate parts: (1) Probability, (2) flow
of water from a hole in a container, (3) the Riccati differential
equation, and (4) a geometry question concerning figures bounded by two
arcs of a circle. These papers won him a position at the influential Academy
of Sciences in St. Petersburg, Russia. At the academy Bernoulli lectured
in medicine, mechanics, and physics. He developed what is now called
Bernoulli's principle: The pressure in a fluid decreases as its velocity
increases.
The modern kinetic
molecular theory of gases essentially started with Bernoulli's suggestion
in 1734 that the pressure exerted by a gas on the walls of its container
is the sum of the many collisions by individual molecules, all moving
independently of each other. Bernoulli derived the basic laws
for the theory of gases and gave, although not in full detail, the equation
of state discovered by van der Waals a century later.
Temperature Scale
Measurement of temperature has developed relatively recently
in human history. The invention of the thermometer is generally credited
to Galileo
who developed the first known thermometer (1592) based on the expansion/contraction
of air. German physicist Fahrenheit
made a mercury
thermometer (1714) ranging from the freezing of water (32°) to
body temperature (96°). Swedish astronomer Celsius
(1742) devised a scale ranging from the boiling of water (0°) to the
freezing of water (100°)--this inverted scale (centigrade) gained widespread
use and in 1948 the name was changed to Celsius. In 1848 British
physicist William
Thomson (Lord Kelvin) proposed a system using degree Celsius but starting
at zero Kelvin (-273°C).
Charles' Law: V1T2=V2T1
Jacques
Charles (1746-1823)
The physical principle known as Charles'
Law states that the volume of a gas equals a constant value multiplied
by its temperature as measured on the Kelvin scale. The law's name honors
the pioneer balloonist Jacques Charles, who in 1787 did experiments on
how the volume of gases depended on temperature. The irony is that
Charles (see photo) never published the work
for which he is remembered, nor was he the first or last to make this discovery.
In fact, Amontons had done the same sorts of experiments 100 years earlier,
and it was Gay-Lussac in 1808 who made definitive measurements and published
results showing that every gas he tested obeyed this generalization.
Law of Combining Volumes
Joseph
Gay-Lussac (1778-1850)
Gay-Lussac (see photo) carefully investigated
the ratio of the volume of hydrogen gas that combined with a given volume
of oxygen gas to form water. He found the oxygen could combine with exactly
twice its own volume of hydrogen. There were similar simple volumetric
ratios for other reactions between gases and if the product of the reaction
was also a gas, it filled a volume simply related to those of the combining
gases.
Gay-Lussac combined research with his passion of hot air balloons.
Because nitrogen is lighter than oxygen, Gay-Lussac reasoned there
might be proportionately less oxygen in the air at higher elevations. To
find out, in 1802 he went up in a balloon to 23,000 feet (a record for
50 years). He found the proportions nearly the same.
Law of Partial Pressures: PT
= P1 + P2 + P3 + ...
John
Dalton (1766-1844)
Dalton's law of partial pressures was stated by John Dalton (see
photo) in 1801: The total pressure of a mixture of gases is equal to
the sum of the partial pressures of the individual component gases.
The partial pressure is the pressure that each gas would exert if it alone
occupied the volume of the mixture at the same temperature.
Avogadro's Principle
Amedeo
Avogadro (1776-1856)
After practicing law for three years, Avogadro (see
photo) began to study mathematics and physics. Eventually he was appointed
Professor of Natural Philosophy at the College of Vercelli. Based on the
work of Gay-Lussac, all gases when subjected to an equal rise in temperature
expand by the same amount, Avogadro published an article (1811) stating
that at the same temperature and pressure, equal volumes of different gases
contain the same number of molecules. The science community
was not ready to accept such a radical idea and Avogadro's Principle went
ignored for the next 50 years. Avogadro's work was finally recognized
when countryman Stanisalo
Cannizaro (see photo) presented the work
at a Conference in 1860. Today, one mole (6.022E23) is called Avogadro's
number. At the time Avogadro's principle was becoming acceptable,
Bernoulli's 1738 kinetic model of tiny gas molecules moving about in otherwise
empty space was also reexamined; our modern view of gases began to emerge
in 1860.
Graham's Law of Effusion: u1/u2
= (m2/m1)½
Thomas
Graham (1805-1869)
Graham (see photo) was professor of chemistry
at University College
in London and later became Master of the Mint. He is best known
for Graham's law (1846) which states that the rate of effusion of a gas
is inversely proportional to the square root of its molecular weight. Graham
also devised the technique known as dialysis to separate colloids from
crystalloids and coined many of the terms used in colloid chemistry.
Molecular Speed: u = (3RT/M)½
James
Clerk Maxwell (1831-1879)
Maxwell (see photo) treated gases statistically
(1866) and formulated what has become known as the root-mean-square
molecular equation (u = [3RT/M]½).
This represents a relationship between molecular mass, average speed,
and temperature (R is the familiar gas constant). Because two
gases with two different masses must have the same average kinetic energy
at the same temperature, the heavier gas molecules must possess lower average
speed.
On another front, Maxwell's mathematical equations expressing the behavior
of electric and magnetic fields are considered one of great achievements
of the 19th century.
Boltzmann Distribution
Ludwig
Boltzmann (1844-1906)
The distribution of velocities among molecules of a gas was first developed
by Maxwell (1859) and later generalized by Boltzmann (1871). The
Maxwell-Boltzmann theory explained the gas laws in terms of the motion
of individual molecules. Previously it was assumed heat flowed from
hot to cold. The Maxwell-Boltzmann theory treated molecules at high
temperature as having a high probability of moving toward those at low
temperature. Consider the distribution of velocities for oxygen at 25°C
shown in the figure: Boltzmann (see photo)
worked out a statistical approach to show more molecules moving at 400
m/s than at any other speed. This type of curve is called a Maxwell-Boltzmann
distribution.
All systems observed to date appear to obey the distribution law.
van der Waals Equation: (P +
a/V2)(V-b) = RT
Johannes
van der Waals (1837-1923)
van der Waals (see photo) began as an elementary
school teacher (1856-1861) but continued with his studies of math and physics.
At age 36 (1873) van der Waals obtained his doctorate and published the
famous equation: (P + a/V2)(V-b)
= RT [for a = b = 0, the equation becomes PV =RT]
The equation considers the specific volume of gas molecules and predicts
critical temperature for condensation. The equation also assumes
a force (van der Waals forces) between molecules. In 1910 van der
Waals awarded Nobel Prize for Physics.
