Name: gas behavior in the equation of state
Uploaded: 2023-09-18T17:11:15.000Z
Duration: 1 min 7 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Physical Science

SC.912.P.12

SC.912.P.12.10

Equation of State

For any thermodynamic system, the state of matter is described by the physical variables pressure, volume, temperature, and total mass of the matter or number of moles.
These physical variables are called state variables, and an equation that relates these physical variables with each other is termed the equation of state.
For example, consider a kettle filled with water. The state of the water inside the kettle is defined by the initial volume, pressure, and temperature. If the water is heated, the volume occupied by the water increases with temperature.
The heated water, converted to steam, occupies a larger volume at the top of the kettle and exerts high pressure on the water. This excess pressure is released when steam leaks out of the spout.
The steam, the gaseous water, is described by new values of these state variables.&#160;
The state of matter can be changed by changing one of the state variables, which causes a change in the other state variables.

equation of state

The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and numerical tables are used to study the relationship between different physical quantities.
Consider a gas cylinder having initial pressure and volume at room temperature. Now, if this gas cylinder is heated to a higher temperature, the pressure exerted by the gas molecule on the walls of the container increases. At a high enough temperature, the gas cylinder explodes. Here the change in temperature of the gas changes the pressure exerted by the gas molecules on the walls of the container. Any change in one of the physical quantities changes the other physical quantities, which defines the equation of state. The equation of state uses macroscopic properties to represent the state/condition of the matter in which it exists.

The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics ...

Education

JoVE Core

Physics

Unit 1

The Kinetic Theory of Gases

KEY TERMS AND CONCEPTS

gas behavior in the equation of state

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system.

The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists.

When an equation of state cannot be written mathematically, scientists use experimental data and numerical tables to study the pattern. A gas cylinder gives a clear example. If the gas starts at room temperature and is heated, the pressure on the walls of the container increases. At a high enough temperature, the cylinder can explode. This shows that a change in one physical quantity changes the others as well.

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

Gas Laws Behind the Ideal Equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

van der waals equation

How Real Gases Deviate from Ideal Behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects. One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a. The second...

pv-diagrams

Liquid-Gas Changes on pV Curves

pV curves show how gas pressure changes with volume. A pV diagram is a graph of pressure versus volume for the gas being studied. It helps describe how the substance behaves. When the gas acts like an ideal gas, the ideal gas equation gives the link between pressure and volume. A common pV curve is an isotherm, which is a line drawn at fixed temperature and fixed number of molecules. For an ideal gas, pressure times volume stays constant. That means volume goes down as pressure goes up. The...

kinetic theory of an ideal gas

Avogadro's Number and Gas Particle Motion

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is. Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number...

molecular kinetic energy

Gas Pressure and Molecular Motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

distribution of molecular speeds

Molecular Speed Curves and Vapor Pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

mean free path and mean free time

Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

escape velocities of gases

Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

key terms and concepts

Learn how pressure, volume, temperature, and moles are linked in an equation of state, with a gas cylinder example that shows how heating changes pressure.

Gas Behavior in the Equation of State | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Georgia Standards of Excellence

9-12

Chemistry

SC5.

gas-laws-pressure-volume-temperature-and-moles

Gas Laws: Pressure, Volume, Temperature, and Moles

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SC.912.P.12.1

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Instantaneous Velocity - II

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Average Acceleration

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Instantaneous Acceleration

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Kinematic Equations - II

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Kinematic Equations - III

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Velocity and Position by Integral Method

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Relative Velocity in One Dimension

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SC.912.P.12.2

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Newton's Second Law

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A. Motion can be measured and described qualitatively and quantitatively. Net forces create a change in motion. When objects travel at speeds comparable to the speed of light, Einstein's special theory of relativity applies.

B. Momentum is conserved under well-defined conditions. A change in momentum occurs when a net force is applied to an object over a time interval.

C. The Law of Universal Gravitation states that gravitational forces act on all objects irrespective of their size and position.

D. Gases consist of great numbers of molecules moving in all directions. The behavior of gases can be modeled by the kinetic molecular theory.

E. Chemical reaction rates change with conditions under which they occur. Chemical equilibrium is a dynamic state in which forward and reverse processes occur at the same rates.

Gas Behavior in the Equation of State

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