# Why do we study or learn about ideal gases?

#### nineteen

We are learning the lesson about gases/gaseous states at our school and I couldn't help but wonder, why learn about IDEAL GASES...... How do ideal gases help us to analyze about real gases?

#### mjc123

Well, you could study lots of tables of experimental P,V,T data. But that's a lot of numbers, and wouldn't give you much understanding.

The ideal gas is a simple model that often (not always) gives a good approximation to the behaviour of real gases, in terms of a few basic physical principles, that hopefully gives the student an insight into the basic processes going on in gases, and how these affect their physical properties. When the behaviour of real gases is not ideal, it is often convenient to treat it as ideal with some small deviations due to factors not taken account of in the ideal model. Thus the van der Waals equation has terms to correct for the volume of the molecules and the intermolecular forces, both of which are relatively very small in near-ideal conditions. The vdW equation is itself a model, not an exact description of a real gas. The only such description is experimental data, but that in itself doesn't give understanding, as I said, or make it easy to predict the properties in different conditions. A model, such as the ideal gas or van der Waals gas, helps to do that. that is what makes it science as distinct from mere observation.

#### nineteen

Well, you could study lots of tables of experimental P,V,T data. But that's a lot of numbers, and wouldn't give you much understanding.

The ideal gas is a simple model that often (not always) gives a good approximation to the behaviour of real gases, in terms of a few basic physical principles, that hopefully gives the student an insight into the basic processes going on in gases, and how these affect their physical properties. When the behaviour of real gases is not ideal, it is often convenient to treat it as ideal with some small deviations due to factors not taken account of in the ideal model. Thus the van der Waals equation has terms to correct for the volume of the molecules and the intermolecular forces, both of which are relatively very small in near-ideal conditions. The vdW equation is itself a model, not an exact description of a real gas. The only such description is experimental data, but that in itself doesn't give understanding, as I said, or make it easy to predict the properties in different conditions. A model, such as the ideal gas or van der Waals gas, helps to do that. that is what makes it science as distinct from mere observation.
Thank you very much for helping. I really appreciate it.

#### Christopher Grayce

There are three reasons: first, gases are generally only significantly nonideal near their boiling point. Most of the gases you encounter in everyday life (or everyday chemistry) are quite far from their boiling points, and behave very nearly ideally for most practical purposes. It's somewhat unusual to need more accuracy than the ideal gas laws give you if you are just doing general chemistry (although you easily might if you are working in some specialized field of chemistry or engineering).

The second reason is because when you study thermodynamics, and later statistical mechanics, a large proportion of the ideas can only be practically illustrated for systems of ideal gases. For nonideal systems, in particular liquids or solids, the math calculations can't be done by hand, so there's no way to show you how the principles of thermo or stat mech work out. Hence, in order to learn thermodynamics and statistical mechanics, you have to understand ideal gases, so you have a system to which you can apply the principles and see how they work out mathematically.

The third reason is more subtle: ideal gases represent the most important kind of complex "many-body" system. (A "many body" system is just what it sounds like, a system with many things that can vary, often atoms and molecules that can be in various places and traveling, rotating, vibrating at different speeds. Pretty much anything bigger than handful of atoms and molecules is a "many body" system, so anything interesting to chemistry or biology.) Ideal gases are many body systems where all the complex math of thermo and stat mech (see above) works out exactly. That means they are very good *starting points* for more complex calculations. Often you can represent some complex system as a slight deviation from an ideal gas system, and there are math techniques for calculating the deviations methodically. Often this is the only way to approach complex systems.

#### Merlin3189

Homework Helper
Gold Member
I've no special knowledge on gas physics, but I'm surprised anyone studying any physics would ask such a question.
It seems to me that most physics is taught starting with ideal models. In mechanics we use point particles, neglect air resistance, have light inextensible strings, light frictionless pulleys, wheels and axles rotate without play, objects may be totally inelastic, etc, etc. In electronics connecting wires are perfect conductors with no inductance or capacitance, inductors and capacitors are pure, power supplies have constant emf and internal resistance, etc. In optics lenses and mirrors have a focus, are thin and of negligible aperture but do not cause diffraction, mirrors are front-silvered.
Just as gases get corrections to the ideal behaviour, we can bring in refinements to take account of more and more of the assumptions of the simplest models, but we always end up with a model, however refined. (That is my opinion - I know some on PF (cleverer than me) disagree.) You have to start somewhere and in modeling, mathematical tractability is crucial.

"Why do we study or learn about ideal gases?"

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