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# Ideal gases

While no ideal gases exist, many gases behave like ideal gases under certain conditions. The concept of an ideal gas is useful for understanding gas behavior and simplifying the calculation of gas properties. This page describes an ideal gas, and develops the ideal gas law and the gas law constant.

## Ideal gas

The kinetic theory of gases postulates that a gas is composed of a large number of very small discrete particles. These particles can be shown to be identified with molecules. For an ideal gas, the volume of these particles is assumed to be so small that it is negligible compared with the total volume occupied by the gas. It is assumed also that these particles or molecules have neither attractive nor repulsive forces between them. The average energy of the particles or molecules can be shown to be a function of temperature only. Thus, the kinetic energy, Ek, is independent of molecule type or size. Because kinetic energy is related to mass and velocity by Ek = 1/2 mv2, it follows that small molecules (less mass) must travel faster than large molecules (more mass) when both are at the same temperature.

## Boyle's law and Charles' law

Molecules are considered to be moving in all directions in a random manner as a result of frequent collisions with one another and with the walls of the containing vessel. The collisions with the walls create the pressure exerted by the gas. Thus, as the volume occupied by the gas is decreased, the collisions of the particles with the walls are more frequent, and an increase in pressure results. It is a statement of Boyle’s law that this increase in pressure is inversely proportional to the change in volume at constant temperature: ....................(1)

where:

• p is the absolute pressure
• V is the volume.

Further, if the temperature is increased, the velocity of the molecules and, therefore, the energy with which they strike the walls of the containing vessel will be increased, resulting in a rise in pressure. To maintain the pressure constant while heating a gas, the volume must be increased in proportion to the change in absolute temperature. This is a statement of Charles’ law, ....................(2)

where:

• T is the absolute temperature
• p is a constant

From a historical viewpoint, the observations of Boyle and Charles in no small degree led to the establishment of the kinetic theory of gases, rather than vice versa. It follows from this discussion that, at zero degrees absolute, the kinetic energy of an ideal gas, as well as its volume and pressure, would be zero. This agrees with the definition of absolute zero, which is the temperature at which all the molecules present have zero kinetic energy.

Because the kinetic energy of a molecule depends only on temperature, and not on size or type of molecule, equal molecular quantities of different gases at the same pressure and temperature would occupy equal volumes. The volume occupied by an ideal gas therefore depends on three things: temperature, pressure, and number of molecules (moles) present. It does not depend on the type of molecule present.

## Ideal gas law

The ideal gas law, which is actually a combination of Boyle’s and Charles’ laws, is a statement of this fact: ....................(3)

where:

• p = pressure
• V = volume
• n = number of moles
• R = gas-law constant
• T = absolute temperature.

## Gas law constant

The gas law constant, R, is a proportionality constant that depends only on the units of p, V, n, and T. Tables 1A through 1C present different values of R for the various units of these parameters. The value of the gas constant is experimental, and more-accurate values are reported occasionally. The values in Tables 1A through 1C are based on the values reported by Moldover et al. Their value was determined from measurements of the speed of sound in argon as a function of pressure at the temperature of the triple point of water. Note that because pV has the units of energy, the value of R is typically given in units of energy per mole per absolute temperature unit [e.g., the appropriate SI value for R is 8.31447 J/(g mol-K), and the appropriate British gravitational (sometimes called the American customary units) value for R is 1,545.35 ft-lbf/(lb-mol°R]. However, sometimes pressure and volume units are more appropriate, such as R = 10.7316 (psia-ft3)/ (lb mol-°R).

## Nomenclature

 Ek = kinetic energy, J m = mass, kg n = number of moles p = absolute pressure, Pa R = gas-law constant, J/(g mol-K) T = absolute temperature, K v = velocity, m/s V = volume, m3