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When we pick up a can of hairspray, how do we know it's safe for us to use it? How did the manufacturers know how much haircare material and gas to pump into it to ensure a controllable release? What about a pressure cooker, the propane tank in the kitchen, or the tires of a car?
We take these thing for granted. But have we ever wondered about laws that govern them? |
"So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity."
W.D. Niven, 'Illustrations of the Dynamical Theory of Gases', 2000
The ideal gas law describes a relationship between pressure, volume, temperature and number of moles in terms of the gas constant for an ideal gas. The ideal gas law assumes that the gas molecules are ideal and do not have any volume and that there are no forces acting on them except during collisions. It was designed to understand the effects of pressure, volume and temperature on gases while excluding the variables of real-world conditions.
The behavior of ideal gases under varying conditions of volume, temperature and pressure in the ideal gas law can be split into the following gas laws: Boyle’s law, Charles’ law and Avogadro’s law. But in order to understand where these laws came from we must first look at the history of the pneumatic sciences, which went through a long, incremental process of trials and errors.
Archimedes of Syracuse (287-212 BCE)
Archimedes was a creative engineer, physicist and mathematician whose seminal contributions to the sciences provided points of entry for the development of Geometry, Calculus, Physics and engineering. Archimedes experiments with buoyancy and density contributed to our understanding of the basic properties of matter.
Galileo Galilei (1564-1642)
Remembered as an astronomer and the scientist who developed fundamental concepts about falling bodies. He was in fact a physicist and an ardent practitioner of the Scientific Method. In one experiment Galileo demonstrated that air had weight (and thus, mass). Galileo also built devices that demonstrated the change in density relative to the change in temperature of a fluid. Through the process of inquiry and experimentation, Galileo opened the door for the slow development of the kinetic theory of gases.
Evangelista Torricelli (1608-1647)
A student of Galileo, who is remembered for developing the Mercury Barometer. More important, Torricelli reasoned from his experiments that we are “Surrounded by an ocean of air” (The earth’s atmosphere) and that this ocean of air can impart a force (weight).
The behavior of ideal gases under varying conditions of volume, temperature and pressure in the ideal gas law can be split into the following gas laws: Boyle’s law, Charles’ law and Avogadro’s law. But in order to understand where these laws came from we must first look at the history of the pneumatic sciences, which went through a long, incremental process of trials and errors.
Archimedes of Syracuse (287-212 BCE)
Archimedes was a creative engineer, physicist and mathematician whose seminal contributions to the sciences provided points of entry for the development of Geometry, Calculus, Physics and engineering. Archimedes experiments with buoyancy and density contributed to our understanding of the basic properties of matter.
Galileo Galilei (1564-1642)
Remembered as an astronomer and the scientist who developed fundamental concepts about falling bodies. He was in fact a physicist and an ardent practitioner of the Scientific Method. In one experiment Galileo demonstrated that air had weight (and thus, mass). Galileo also built devices that demonstrated the change in density relative to the change in temperature of a fluid. Through the process of inquiry and experimentation, Galileo opened the door for the slow development of the kinetic theory of gases.
Evangelista Torricelli (1608-1647)
A student of Galileo, who is remembered for developing the Mercury Barometer. More important, Torricelli reasoned from his experiments that we are “Surrounded by an ocean of air” (The earth’s atmosphere) and that this ocean of air can impart a force (weight).
Archimedes
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Galileo
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Torricelli
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Blaise Pascal (1623-1662)
Blaise Pascal died young, but in one brief period of scientific creativity he authored a book on Geometry, invented a calculating machine that was a precursor to the computer, laid the foundation for probability theory and laid the conceptual framework for the independent discoveries of Archimedes (buoyancy) , Galileo (weight of air) and Torricelli the weight of the ocean of air in which we live). His observations led to the conclusion:
Pressure in a confined fluid (and gas) is transmitted equally and undiminished in all directions. In a single statement he defined a new term, pressure, and he expressed it as a simple mathematical relationship: Pressure (P) = Force(F) per unit Area(A), or P = F/A.
Understanding this simple algebraic expression will allow us to mathematically model and predict the performance of the pneumatic systems we design. This simple algebraic expression explains how it is possible to dramatically multiply forces within cylinders and transmit them significant distances through tubes and circuits within a pneumatic system.
Robert Boyle (1627-1691)
While he is popularly regarded as the father of modern chemistry, Boyle made many significant contributions to the field of physics. Not least of which is a physical law that bears his name. Boyle realized that the product of the pressure and the volume within a closed system was constant (PV=k). He also noted that within a closed system, the pressure of a gas varies inversely with respect to volume. Increase the volume, and the pressure drops. Conversely if the volume is decreased, the pressure rises.
What Robert Boyle gave us was more than just an observation. He gave us the one of the essential tools of pneumatic engineering. Boyle provided us with a tool that could be used to mathematically predict the behavior of a system. Let’s look at the implication of what Pascal observed and what Boyle quantified.
Pascal noted that pressure was a force acting equally throughout a fluid or a gas. Boyle explained that if we reduce the volume of a given amount of gas by 1/2 then we double the pressure. The pressure is then doubled and acts equally on all surfaces of the contained gas! The development of a universal gas law was nearing completion.
Jacques Charles (1746-1823)
Jacques Charles enjoyed experimenting, and he was a daring inventor. In 1783 he heard news that the Montgolfier brothers had flown in a gas balloon. It is not certain that he knew they had used hot air to create the necessary buoyancy. He began to ponder how they may have accomplished this feat. He reasons they had filled the necessary volume with hydrogen, a recently discovered gas that was more than 10 times lighter than air. After several experiments Jacques Charles accomplished his solo flight in a hydrogen filled balloon!
Jacques Charles provided some key components necessary to formulate the ideal gas law. He performed experiments that that allowed him to conclude that Pressure was proportional to temperature: Pressure = Temperature x K (a constant).
Jacques Charles quantitatively measured the relationship between temperature and pressure in a fixed amount of gas, and found the two quantities to have a proportional relationship. That is to say that a graph of changes in temperature with changes in volume forms a straight line.
Jacques however used a Celsius scale. In this case the proportionality was not a direct proportion. The line of a graph plotting the change in Celsius temperature plotted against a change in volume did not pass through the origin of is temperature and pressure graph (0 degrees Celsius/0 cm3). It was not until Lord Kelvin discovered that if he added 273 to every degree Celsius, that the proportionality of volume and temperature in a fixed amount of gas became a direct proportion! The concept of absolute temperature was another step towards defining the ideal gas law.
If temperature affected the volume or pressure of a gas, the implication was clear. Gases, at their fundamental molecular levels, are mechanical in nature, and the laws of kinematics could help predict the behavior of gases.
This algebraic tool allows us to predict the effects of changes in temperature, volume and pressure within a closed pneumatic system.
While temperature is certainly a factor in controlling pressure, this fact will not be considered in the problems that follow. Students are not expected to have temperature controls on their pneumatic systems. Never attempt to increase pressure by heating pressurized gas reservoirs.
Blaise Pascal died young, but in one brief period of scientific creativity he authored a book on Geometry, invented a calculating machine that was a precursor to the computer, laid the foundation for probability theory and laid the conceptual framework for the independent discoveries of Archimedes (buoyancy) , Galileo (weight of air) and Torricelli the weight of the ocean of air in which we live). His observations led to the conclusion:
Pressure in a confined fluid (and gas) is transmitted equally and undiminished in all directions. In a single statement he defined a new term, pressure, and he expressed it as a simple mathematical relationship: Pressure (P) = Force(F) per unit Area(A), or P = F/A.
Understanding this simple algebraic expression will allow us to mathematically model and predict the performance of the pneumatic systems we design. This simple algebraic expression explains how it is possible to dramatically multiply forces within cylinders and transmit them significant distances through tubes and circuits within a pneumatic system.
Robert Boyle (1627-1691)
While he is popularly regarded as the father of modern chemistry, Boyle made many significant contributions to the field of physics. Not least of which is a physical law that bears his name. Boyle realized that the product of the pressure and the volume within a closed system was constant (PV=k). He also noted that within a closed system, the pressure of a gas varies inversely with respect to volume. Increase the volume, and the pressure drops. Conversely if the volume is decreased, the pressure rises.
What Robert Boyle gave us was more than just an observation. He gave us the one of the essential tools of pneumatic engineering. Boyle provided us with a tool that could be used to mathematically predict the behavior of a system. Let’s look at the implication of what Pascal observed and what Boyle quantified.
Pascal noted that pressure was a force acting equally throughout a fluid or a gas. Boyle explained that if we reduce the volume of a given amount of gas by 1/2 then we double the pressure. The pressure is then doubled and acts equally on all surfaces of the contained gas! The development of a universal gas law was nearing completion.
Jacques Charles (1746-1823)
Jacques Charles enjoyed experimenting, and he was a daring inventor. In 1783 he heard news that the Montgolfier brothers had flown in a gas balloon. It is not certain that he knew they had used hot air to create the necessary buoyancy. He began to ponder how they may have accomplished this feat. He reasons they had filled the necessary volume with hydrogen, a recently discovered gas that was more than 10 times lighter than air. After several experiments Jacques Charles accomplished his solo flight in a hydrogen filled balloon!
Jacques Charles provided some key components necessary to formulate the ideal gas law. He performed experiments that that allowed him to conclude that Pressure was proportional to temperature: Pressure = Temperature x K (a constant).
Jacques Charles quantitatively measured the relationship between temperature and pressure in a fixed amount of gas, and found the two quantities to have a proportional relationship. That is to say that a graph of changes in temperature with changes in volume forms a straight line.
Jacques however used a Celsius scale. In this case the proportionality was not a direct proportion. The line of a graph plotting the change in Celsius temperature plotted against a change in volume did not pass through the origin of is temperature and pressure graph (0 degrees Celsius/0 cm3). It was not until Lord Kelvin discovered that if he added 273 to every degree Celsius, that the proportionality of volume and temperature in a fixed amount of gas became a direct proportion! The concept of absolute temperature was another step towards defining the ideal gas law.
If temperature affected the volume or pressure of a gas, the implication was clear. Gases, at their fundamental molecular levels, are mechanical in nature, and the laws of kinematics could help predict the behavior of gases.
This algebraic tool allows us to predict the effects of changes in temperature, volume and pressure within a closed pneumatic system.
While temperature is certainly a factor in controlling pressure, this fact will not be considered in the problems that follow. Students are not expected to have temperature controls on their pneumatic systems. Never attempt to increase pressure by heating pressurized gas reservoirs.
Pascal
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Boyle
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Charles
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Amadeo Avogadro (1776-1856)
Amedeo Avogadro was, like many great scientists of his era, both a physicist and a chemist. He is credited with having coined the word molecule, and establishing the formula for water, H2O. Avogadro’s contribution to pneumatics lies in his most remembered work, the establishment of a law that bears his name, as well as a fundamentally important concept, Avogadro’s number.
Avogadro’s law states that equal volumes of different gases at the same temperature and pressure contain equal number of molecules! Avogadro’s Number 6.02 * 10^23 This number refers to the number of molecules of a gas at standard temperature and pressure.
The volume occupied by one mole of any gas at Standard Temperature and Pressure is called its molar volume. This volume is the same for all gases. This volume is equal to 22.4 liters (a little more than 3/4 of a cubic foot).
The gram weight of the molar volume of any gas molecule can be found by adding the atomic weights of the atoms that combine to make the gas molecule.
A molar volume is always 22.4 liters. With this information we can compute the grams per liter of any gas as well as the weight of any quantity of any gas whose molecular formula is known.
Avogadro’s research contributed to the development of the Ideal Gas Equation. The Ideal Gas Equation describes the relationship between pressure, temperature and volume, and provides engineers with the tools they need to mathematically predict the behavior of gases under a variety of conditions.
Emil Clapeyron (1799-1864)
Emil Claperyon is credited with having formulated the ideal gas law in 1834. Take a minute to look at the algebra that describes the relationship between Pressure, Volume, Temperature and the quantity of gas in a system. This simple statement represents the culmination of the work of dozens of scientists over hundreds of years and it includes the discoveries of the scientists recognized in this lesson.
The Ideal Gas Equation
PV = nRT
Where:
P = pressure in atmospheres
V = volume in liters
n = moles
R = Ideal gas constant = 0.0821 liter* atmospheres/mole* Kelvin
T = Temperature in degrees Kelvin
The understanding exhibited by this simple equation is used by men and women who design and manufacture safe reliable pneumatic systems. The fundamental laws that govern gas behavior were discovered sequentially by men and women who made incremental contributions to development of our understanding of the behavior of gasses. Each in turn, contributed to this growing body of knowledge. This is a story of pneumatic science, and it is representative of the story of science in general.
Amedeo Avogadro was, like many great scientists of his era, both a physicist and a chemist. He is credited with having coined the word molecule, and establishing the formula for water, H2O. Avogadro’s contribution to pneumatics lies in his most remembered work, the establishment of a law that bears his name, as well as a fundamentally important concept, Avogadro’s number.
Avogadro’s law states that equal volumes of different gases at the same temperature and pressure contain equal number of molecules! Avogadro’s Number 6.02 * 10^23 This number refers to the number of molecules of a gas at standard temperature and pressure.
The volume occupied by one mole of any gas at Standard Temperature and Pressure is called its molar volume. This volume is the same for all gases. This volume is equal to 22.4 liters (a little more than 3/4 of a cubic foot).
The gram weight of the molar volume of any gas molecule can be found by adding the atomic weights of the atoms that combine to make the gas molecule.
A molar volume is always 22.4 liters. With this information we can compute the grams per liter of any gas as well as the weight of any quantity of any gas whose molecular formula is known.
Avogadro’s research contributed to the development of the Ideal Gas Equation. The Ideal Gas Equation describes the relationship between pressure, temperature and volume, and provides engineers with the tools they need to mathematically predict the behavior of gases under a variety of conditions.
Emil Clapeyron (1799-1864)
Emil Claperyon is credited with having formulated the ideal gas law in 1834. Take a minute to look at the algebra that describes the relationship between Pressure, Volume, Temperature and the quantity of gas in a system. This simple statement represents the culmination of the work of dozens of scientists over hundreds of years and it includes the discoveries of the scientists recognized in this lesson.
The Ideal Gas Equation
PV = nRT
Where:
P = pressure in atmospheres
V = volume in liters
n = moles
R = Ideal gas constant = 0.0821 liter* atmospheres/mole* Kelvin
T = Temperature in degrees Kelvin
The understanding exhibited by this simple equation is used by men and women who design and manufacture safe reliable pneumatic systems. The fundamental laws that govern gas behavior were discovered sequentially by men and women who made incremental contributions to development of our understanding of the behavior of gasses. Each in turn, contributed to this growing body of knowledge. This is a story of pneumatic science, and it is representative of the story of science in general.
Ponder this
It was mentioned that gasses are mechanic in nature, what does it mean by this? How is it proven?
How do we manipulate the Ideal Gas Law for practical purposes, considering the variables involved? Have we applied such things?
Discuss
The Ideal Gas Law implies that in practice, gasses do not perform as expected. This is not surprising as the many variables (pressure, volume, temperature) do not react to each other's inputs immediately or perfectly. What sort of applications that proves this?
Further readings
The Gas Laws, courtesy of the College of Science at Purdue University.
Archimedes, Galileo, Torricelli, Pascal, Boyle, Charles, Avogadro and Clapeyron, short primers on their life and works.
"London's Victorian Hyperloop", an article on the application of pneumatic principles during the Victorian Era.
