Bernoulli Proposes the Kinetic Theory of Gases Summary

  • Last updated on November 10, 2022

Daniel Bernoulli developed the first systematic theory to explain the behavior of gases in terms of their kinetic (or motion-related) properties. Using a mathematical approach, he established a formal relationship between, on the one hand, the many tiny collisions between individual gas molecules and the walls of a container and, on the other hand, the overall pressure exerted on the container by the gas taken as a whole.

Summary of Event

By the seventeenth century, scientists had noted that gases had unusual properties that they could not explain. In particular, gases were fluids in the sense that they could flow and fill a volume having an irregular shape, but they could also exert a force on the walls of a closed container. This latter property of gases was easily demonstrated placing a gas in a container that was capped by a piston and noting that the piston was supported by the gas. [kw]Bernoulli Proposes the Kinetic Theory of Gases (1738) [kw]Gases, Bernoulli Proposes the Kinetic Theory of (1738) [kw]Theory of Gases, Bernoulli Proposes the Kinetic (1738) [kw]Kinetic Theory of Gases, Bernoulli Proposes the (1738) Gases Kinetic theory of gases [g]Russia;1738: Bernoulli Proposes the Kinetic Theory of Gases[0930] [c]Chemistry;1738: Bernoulli Proposes the Kinetic Theory of Gases[0930] [c]Physics;1738: Bernoulli Proposes the Kinetic Theory of Gases[0930] [c]Science and technology;1738: Bernoulli Proposes the Kinetic Theory of Gases[0930] Bernoulli, Daniel Boyle, Robert

The Irish chemist Robert Boyle took the first step in developing a theory to explain some of the properties of a gas. Boyle was a careful experimentalist, and he studied the behavior of a gas held in a container topped by a piston. He kept the container and the gas at a constant temperature and measured the gas’s volume and pressure, that is, the force exerted on the piston divided by the area of the piston. In 1660, Boyle published the results of a series of measurements of the pressure and volume of a gas that was held at a constant temperature. These results demonstrated that the volume of a gas is inversely proportional to the pressure it exerts, a result now known as Boyle’s law. Boyle’s law (chemistry)[Boyles law]

Prior to Boyle’s measurements, physicists had studied the mechanical properties of springs. It was well established that the force required to compress a spring increased linearly as the spring got shorter. Boyle suggested that the length of a spring was analogous to the volume of a gas inside a container, and the force exerted by the spring was analogous to the force exerted by the gas against the container. Thus, Boyle suggested, gases were in some sense springs that, when they were compressed or distorted, exerted a force proportional to their degree of compression. Boyle was also aware that the volume of a gas increases when the gas is heated. However, he was not able to determine a mathematical relationship between a gas’s temperature and its volume, because there was no well-established temperature scale Temperature scales in Boyle’s era. It was the development of accurate and reproducible thermometers Thermometers by the German scientist Daniel Gabriel Fahrenheit, Fahrenheit, Daniel Gabriel who invented the mercury thermometer in 1714, that allowed the relationship between temperature and volume to be precisely determined.

Working from Boyle’s law as a starting point, the Dutch-born Swiss mathematician and physicist Daniel Bernoulli attempted to determine the physical cause of which the law was an effect. Bernoulli, who was teaching in St. Petersburg, Russia, at the time, became the first scientist to understand air pressure in terms of the behavior of the individual molecules making up the air. Unlike Boyle, who took a careful series of measurements, Bernoulli took a theoretical approach to explaining the pressure exerted by a gas. He considered a cylinder that was oriented vertically, was sealed at the bottom, and had a piston at the top. The piston, which was free to move up and down but which would not allow gas to escape, had a weight on top of it. The piston and weight were supported by the pressure of the gas inside the cylinder.

Bernoulli proposed that a gas was composed of individual objects, Matter;and motion[motion] Motion;and matter[matter] which are now called molecules, that move very rapidly, colliding with the surface of the piston. When they hit the piston, the molecules are reflected back in the opposite direction. Each collision exerts a minute force on the piston. The macroscopic pressure exerted by the gas on the piston represents the sum of the force of all these minute collisions. Thus, the gas behaves as a fluid, expanding to occupy more volume as the piston is moved upward, increasing the available volume of the container. However, if the speed of the molecules remains constant, then as the volume of the container increases, the time required for an individual gas molecule to move across the container and strike the piston also increases. There are therefore fewer collisions in any given time interval, and the pressure exerted on the piston decreases proportionally. Bernoulli’s model, published as a chapter in his Hydrodynamica (1738; Hydrodynamics, Hydrodynamics (Bernoulli) 1968), is called a “kinetic theory,” Kinetic theory of gases because the macroscopic properties of the gas depend on molecular motion.

Bernoulli’s kinetic theory was not widely accepted at the time. Most scientists believed that the molecules in a gas stayed more or less in place, repelling each other from a distance by the action of some unknown force. The British physicist Sir Isaac Newton Newton, Sir Isaac Newton, Sir Isaac;theory of motion[motion] had shown that the inverse relationship between pressure and volume of a gas could follow simply from an inverse-square law of repulsion between the gas molecules. Thus, in Bernoulli’s era, the accepted model was that gas molecules were essentially fixed in position. This, too, may have been a function of the relative dearth of rigorous temperature-related experimentation, as the intimate relationship between temperature and kinetic energy was entirely unknown.

One weakness in Bernoulli’s kinetic theory was that the speeds of the individual molecules in a gas could not be measured; thus, the pressure each molecule exerted on a piston could not be calculated. Bernoulli understood that it was not necessary to determine the speed of each molecule. The macroscopic pressure could be determined simply by knowing the average speed of the molecules, the mass of the molecules, and the rate of collision. Bernoulli, however, was not able to determine the relationship of the speed of a gas molecule to its temperature, which, like pressure and volume, was a measurable macroscopic property.

Significance

It was not until the 1850’s that the link posited by Bernoulli between the properties of the individual molecules making up a gas and the macroscopic behavior of the gas gained widespread acceptance in the scientific community. In 1859, the Scottish physicist James Clerk Maxwell [p]Maxwell, James Clerk attacked the problem. Maxwell adopted Bernoulli’s model of gas molecules as perfectly “elastic particles” (that is, particles that obey Sir Isaac Newton’s laws of motion but that lose no energy when they collide with each other or with other objects). Maxwell quickly recognized that even a small container of gas held far too many molecules to permit him to analyze this system completely using Newton’s laws. However, Maxwell also realized that he simply needed to understand in principle how the microscopic picture of molecules in motion was connected with gases’ macroscopic properties, which represented averages over extremely large numbers of molecules. Using a statistical approach, Maxwell was able to find the “velocity distribution function,” that is, a function to determine the number of gas molecules that have a given velocity for gases at a fixed temperature.

Once Bernoulli’s kinetic theory of gases gained widespread acceptance, it had a major impact on how theoretical physicists attempted to understand the large-scale physical properties of objects. Bernoulli’s work introduced several new ideas to the world of physics. In developing the first kinetic theory of gases, he proposed that the macroscopic properties of objects are due to and can be explained by the motion and behavior of the particles that make up those objects.

Thus, Bernoulli showed that by considering the behavior of the atomic and molecular constituents of matter, the large-scale physical properties of matter can be understood. This concept was important in many areas of physics: for example, the subsequent understanding of conduction of electricity, heat, and sound through matter. Bernoulli, moreover, expressed the results of his theory in terms of statistics. Statistics would arise as a science in its own right in the nineteenth century, and the use of statistical formulations in the physical sciences would become more acceptable thereafter. Statistical physics would become particularly important with the development in the twentieth century of quantum mechanics, a field of physics in which all of the properties of the particles that make up an object are expressed in probabilistic terms.

Bernoulli’s work also paved the way for the modern understanding of the behavior of gases, developed by Johannes Diderik van der Waals Waals, Johannes Diderik van der . Van der Waals related pressure, volume, and temperature in an equation that extended the results obtained by Bernoulli to include the finite size of gas molecules and the small attractive force between the molecules, now called the van der Waals force. Van der Waals was awarded the Nobel Prize in Physics in 1910 for this work.

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Asimov, Isaac. The History of Physics. New York: Walker, 1966. Designed for nonspecialists; Asimov includes an excellent section, “The Kinetic Theory of Gases,” which describes Bernoulli’s contribution and puts that contribution in the historical context of both prior and subsequent work on the behavior of gases.
  • citation-type="booksimple"

    xlink:type="simple">Brush, Stephen G., and Nancy S. Hall. Kinetic Theory of Gases: An Anthology of Classic Papers with Historical Commentary. London: Imperial College Press, 2003. This 661-page anthology contains more than two dozen papers on the kinetic theory of gases. It includes Bernoulli’s “On the Properties and Motions of Elastic Fluids,” excerpted from Hydrodynamics, as well as Boyle’s concept of a “spring of the air,” Newton’s repulsion theory, and Maxwell’s “Dynamical Theory of Gases.” In addition to reprinting the classic papers, the book includes five essays providing historical commentary on the kinetic theory of gases and thermodynamics.
  • citation-type="booksimple"

    xlink:type="simple">Ehrenfest, Paul, and Tatiana Ehrenfest. The Conceptual Foundations of the Statistical Approach in Mechanics. Mineola, N.Y.: Dover, 2002. Although somewhat technical, this Dover reprint of Ehrenfest’s 1912 article from the German Encyclopedia of Mathematical Sciences describes the foundations of kinetic theory and statistical mechanics.

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