# Ideal gases Definition and 7 Discussions

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.
Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.710947(13) litres at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 105 Pa) as defined by IUPAC since 1982.The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size becomes important. It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor. At high pressures, the volume of a real gas is often considerably larger than that of an ideal gas. At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid. The model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state. The deviation from the ideal gas behavior can be described by a dimensionless quantity, the compressibility factor, Z.
The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.
If the pressure of an ideal gas is reduced in a throttling process the temperature of the gas does not change. (If the pressure of a real gas is reduced in a throttling process, its temperature either falls or rises, depending on whether its Joule–Thomson coefficient is positive or negative.)

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1. ### B Collision time interval of a gas molecule with wall of container

I have been trying to make sense of the derivation of pressure under Kinetic Theory of Gases chapter, but it's not making sense to me when the impulse momentum equation is used for the collision between a gas molecule and the wall of the container. The book says that for the elastic collision...
2. ### How could the discrepancy be reduced between the two readings?

I am able to solve part (a) using the relationship ##\frac {P_1} {T_1} = \frac {P_2} {T_1}##, where ##T_1 = 273.16## since its the triple point of water and ##T_2 =T_s## ##(T_s = ## melting point of sulphur). I use the two readings for thermometer A to get ##P_1## and ##P_2## as mentioned in the...
3. ### B Confusion when considering pV=nRT in Two Balloon experiment

This is the Two-Balloon Experiment: https://en.wikipedia.org/wiki/Two-balloon_experiment#cite_note-MW78-1 The claim on Wikipedia which I am a little confused over is that when 2 balloons (at the 2 red points) are connected via a tube, the smaller balloon at a higher pressure would push air...
4. ### I Question regarding dh, du, cp, cv for ideal gases

Hi, Considering the question bellow from a government work selection process: Check the FALSE alternative on the use of thermodynamic properties. In a cylinder-piston type system, the variation of the enthalpy property (Δh) is usually applied to determine the heat (per kilogram) exchanged...
5. ### Find the change in the Kinetic energy of an Ideal Gas

Homework Statement Let 3/2kT be the kinetic energy of ideal gas per molecules. T the absolute temperature and N the avogadro number. Answer the following questions : 1) when the volume doubled at constant temperature. How many times the kinetic energy per molecule become greater than before...
6. ### Gas Laws -- why calculate the mean square speed at 273K?

Homework Statement Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K? Why 273K?
7. ### Modeling index of refraction of dilute gases

I'm interested in predicting the index of refraction of atmospheric air and several nonpolar gases at room temperature for pressures of 1 atm - 0 atm. I'm not really sure where to get started. I have found the relation n=\sqrt{1+\frac{3AP}{RT}} but I don't really get where it comes from. Well...