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While no ideal gases exist, many gases behave like ideal gases under certain conditions. | 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, ''E''<sub>''k''</sub>, is independent of molecule type or size. Because kinetic energy is related to mass and velocity by ''E''<sub>''k''</sub> = 1/2 ''mv''<sup>2</sup>, it follows that small molecules (less mass) must travel faster than large molecules (more mass) when both are at the same temperature. | 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, ''E''<sub>''k''</sub>, is independent of molecule type or size. Because kinetic energy is related to mass and velocity by ''E''<sub>''k''</sub> = 1/2 ''mv''<sup>2</sup>, 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 == | == 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: | 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: | ||
[[File:Vol1 page 0218 eq 001.png]]....................(1) | [[File:Vol1 page 0218 eq 001.png|RTENOTITLE]]....................(1) | ||
where: | |||
*''p'' is the absolute pressure | *''p'' is the absolute pressure | ||
*''V'' is the volume. | *''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, | 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, | ||
[[File:Vol1 page 0218 eq 002.png]]....................(2) | [[File:Vol1 page 0218 eq 002.png|RTENOTITLE]]....................(2) | ||
where: | |||
*''T'' is the absolute temperature | *''T'' is the absolute temperature | ||
*''p'' is a constant | *''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. | 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. | 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== | == Ideal gas law == | ||
The ideal gas law, which is actually a combination of Boyle’s and Charles’ laws, is a statement of this fact: | The ideal gas law, which is actually a combination of Boyle’s and Charles’ laws, is a statement of this fact: | ||
[[File:Vol1 page 0218 eq 003.png]]....................(3) | [[File:Vol1 page 0218 eq 003.png|RTENOTITLE]]....................(3) | ||
where: | |||
*''p'' = pressure | *''p'' = pressure | ||
*''V'' = volume | *''V'' = volume | ||
*''n'' = number of moles | *''n'' = number of moles | ||
*''R'' = gas-law constant | *''R'' = gas-law constant | ||
*''T'' = absolute temperature. | *''T'' = absolute temperature. | ||
==Gas law constant== | == Gas law constant == | ||
<gallery widths=300px heights=200px> | 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.''<ref name="r1">Moldover, M.R., Trusler, J.P.M., Edwards, T.J. et al. 1988. Measurement of the Universal Gas Constant R Using a Spherical Acoustic Resonator. J. Res. Nat. Inst. Stand. Technol. 93 (2): 85.</ref> 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-ft<sup>3</sup>)/ (lb mol-°R). | ||
<gallery widths="300px" heights="200px"> | |||
File:Vol1 Page 219 Image 0001.png|'''Table 1A''' | File:Vol1 Page 219 Image 0001.png|'''Table 1A''' | ||
| Line 49: | Line 55: | ||
</gallery> | </gallery> | ||
==Nomenclature== | == Nomenclature == | ||
{| | {| | ||
|- | |- | ||
|''m'' | | ''E''<sub>''k''</sub> | ||
|= | | = | ||
|mass, kg | | kinetic energy, J | ||
|- | |||
| ''m'' | |||
| = | |||
| mass, kg | |||
|- | |- | ||
|''n'' | | ''n'' | ||
|= | | = | ||
|number of moles | | number of moles | ||
|- | |- | ||
|''p'' | | ''p'' | ||
|= | | = | ||
|absolute pressure, Pa | | absolute pressure, Pa | ||
|- | |- | ||
|''R'' | | ''R'' | ||
|= | | = | ||
|gas-law constant, J/(g mol-K) | | gas-law constant, J/(g mol-K) | ||
|- | |- | ||
|''T'' | | ''T'' | ||
|= | | = | ||
|absolute temperature, K | | absolute temperature, K | ||
|- | |- | ||
|''v'' | | ''v'' | ||
|= | | = | ||
|velocity, m/s | | velocity, m/s | ||
|- | |- | ||
|''V'' | | ''V'' | ||
|= | | = | ||
|volume, m<sup>3</sup> | | volume, m<sup>3</sup> | ||
|} | |} | ||
==References== | == References == | ||
<references> | |||
<references /> | |||
== Noteworthy papers in OnePetro == | |||
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | ||
==External links== | == External links == | ||
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | ||
==See also== | == See also == | ||
[[Gas properties]] | |||
[[Gas_properties|Gas properties]] | |||
[[Real_gases|Real gases]] | |||
[[PEH:Gas_Properties]] | |||
==Category== | |||
[[ | [[Category:4.1.4 Gas processing]] [[Category:YR]] | ||
Latest revision as of 11:18, 6 July 2015
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.[1] 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).
Table 1A
Table 1B
Table 1C
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 |
References
- ↑ Moldover, M.R., Trusler, J.P.M., Edwards, T.J. et al. 1988. Measurement of the Universal Gas Constant R Using a Spherical Acoustic Resonator. J. Res. Nat. Inst. Stand. Technol. 93 (2): 85.
Noteworthy papers in OnePetro
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
External links
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro