# Why do we study or learn about ideal gases?

• nineteen
In summary: It seems to me like you're asking why ideal gases are studied, when real gases behave similarly most of the time. The ideal gas is a 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
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?

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.

256bits and nineteen
mjc123 said:
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.

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.

256bits
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.

nineteen and 256bits

## 1. Why is it important to study ideal gases?

Studying ideal gases is important because they serve as a fundamental model for understanding the behavior of real gases. Ideal gases follow simple laws that can be used to predict and explain the properties of real gases, making it easier to understand and work with them in various scientific and industrial applications.

## 2. What are the characteristics of an ideal gas?

An ideal gas is a theoretical gas that follows certain assumptions, including having particles that have no volume, do not interact with each other, and have elastic collisions. It also follows the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are directly proportional to each other.

## 3. How do we apply the study of ideal gases in real life?

The study of ideal gases has many practical applications, such as in the design of engines and other machinery, the production and storage of gases, and the understanding of weather patterns. It also provides a basis for understanding the behavior of real gases, which are present in our everyday lives.

## 4. What are the limitations of the ideal gas model?

The ideal gas model is a simplified representation of real gases and does not account for all factors that may affect their behavior, such as intermolecular forces and the volume of gas particles. It also assumes that gases are at low pressure and high temperature, which may not always be the case.

## 5. How does the study of ideal gases relate to other branches of science?

The study of ideal gases is closely related to other branches of science, such as thermodynamics, chemistry, and meteorology. It provides a foundation for understanding the behavior of gases in these fields and is often used in calculations and experiments to make predictions and draw conclusions.

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