# Definition of an Ideal Gas

Mentor
In another thread, DH and I have been discussing the definition of an ideal gas. DH, who appears to be a physicist, seems to use a definition different from that which we engineers use. I am soliciting responses from both physicists and engineers as to their understanding of the term "ideal gas." I would like to determine whether there really is a difference or not. To get the ball rolling, here is my understanding, as an engineer, of what an ideal gas is:

The term "ideal gas" describes the limiting behavior of a real gas in the limit of low pressures. As such it has the following characteristics:
1. Its PVT behavior is described by PV=nRT
2. Its internal energy and enthalpy are functions only of temperature.
3. Its Cp and Cv can vary with temperature (although for monatomic gases, this variation is negligible).

This definition is in agreement with that given in engineering treatises by Smith and Van Ness (Introduction to Chemical Engineering Thermodynamics), Hougan and Watson, Perry's (Chemical Engineers' Handbook), and Bird, Stewart, and Lightfoot (Transport Phenomena).

I'm hoping that people with engineering backgrounds in particular, like rude man, SteamKing, and maybe, Studiot will respond to this thread and voice their understandings.

Chet

## Answers and Replies

Staff Emeritus
Science Advisor
Engineers. Bah!

To a physicist, PV=nkT (chemists and engineers use PV=NRT) is a derived result rather than a definitional one. It derives from the kinetic theory of gases. An ideal gas is a gas made of negligibly small particles that interact only through elastic collisions, whose velocities are randomly distributed, and energy is equally partitioned. These assumptions are never quite true. Real gases always deviate from the ideal somehow. Physicists call a gas that behaves close to ideal a near-ideal or quasi-ideal gas.

There's a short little sentence buried in the middle of the wikipedia article on ideal gases that contains a term I hadn't heard until now, emphasis mine, but that explains what's going on here:
Sometimes, a distinction is made between an ideal gas, where ĉv and ĉp could vary with temperature, and a perfect gas, for which this is not the case.​

Apparently what physicists call an ideal gas, you engineers would call a perfect gas.

Science Advisor
Gold Member
My background is aerospace engineering. Typically an ideal gas in my field is one that is incompressible, inviscid, non-conducting, and continuous, or in other words, it has no dissipative phenomena and can be described with potential flow theory.

We also define two types of perfect gases: thermally perfect gases and calorically perfect gases. A thermally perfect gas is one where the mean free path is large enough that intermolecular forces can be neglected and the equation of state $p = \rho R T$ holds. A calorically perfect gas is one where the specific heats $c_v$ and $c_p$ are constant (independent of temperature) and you can therefore define a constant ratio of specific heats, $\gamma$, which gets used extensively in compressible flow theory.

I think the definitions of perfect gases are pretty static across fields who use the term. The definition of an ideal gas likely varies depending on what that particular field considers ideal in a gas. For aerospace engineers, the ability to treat a flow field as obeying a potential function is pretty ideal, so our definition has a lot to do with that.

Mentor
Engineers. Bah!

To a physicist, PV=nkT (chemists and engineers use PV=NRT) is a derived result rather than a definitional one. It derives from the kinetic theory of gases. An ideal gas is a gas made of negligibly small particles that interact only through elastic collisions, whose velocities are randomly distributed, and energy is equally partitioned. These assumptions are never quite true. Real gases always deviate from the ideal somehow. Physicists call a gas that behaves close to ideal a near-ideal or quasi-ideal gas.

There's a short little sentence buried in the middle of the wikipedia article on ideal gases that contains a term I hadn't heard until now, emphasis mine, but that explains what's going on here:
Sometimes, a distinction is made between an ideal gas, where ĉv and ĉp could vary with temperature, and a perfect gas, for which this is not the case.​

Apparently what physicists call an ideal gas, you engineers would call a perfect gas.

I think your last two sentences disagree with one another. Please check them out and reconcile.

Regarding your statement that "Apparently what physicists call an ideal gas, you engineers would call a perfect gas." Well,...no. The engineering definition of an ideal gas I gave in post #1 has always been what I've understood to be an ideal gas during my 50 year career as a chemical engineer, and the term "ideal gas" has always been used for a gas which exhibits such behavior in all the prominent chemical engineering texts that I've ever seen. Now, if you physicists would like to change the name of what you call an ideal gas to a perfect gas, that's OK with us engineers. But we'll stick with what we use.

I'm not really surprised that two different scientific disciplines would use the same term to represent two slightly different definitions of material behavior. I've seen the same type of thing with other parameters, such as the stress tensor. But I am surprised that someone would be unwilling to allow for any other possible definition of a term except their own.

Mentor
Briefly, what physicists call an ideal gas, engineers call a perfect gas. I provided a more detailed answer in your thread on this side topic.

Well,...no. The engineering definition of an ideal gas I gave in my previous post has always been what I've understood to be an ideal gas during my 50 year career as a chemical engineer, and the term "ideal gas" has always been used for a gas which exhibits such behavior in all the prominent chemical engineering texts that I've ever seen. Now, if you physicists would like to change the name of what you call an ideal gas to a perfect gas, that's OK with us engineers. But we'll stick with what we use.

Science Advisor
I think your last two sentences disagree with one another. Please check them out and reconcile.

Regarding your statement that "Apparently what physicists call an ideal gas, you engineers would call a perfect gas." Well,...no. The engineering definition of an ideal gas I gave in post #1 has always been what I've understood to be an ideal gas during my 50 year career as a chemical engineer, and the term "ideal gas" has always been used for a gas which exhibits such behavior in all the prominent chemical engineering texts that I've ever seen. Now, if you physicists would like to change the name of what you call an ideal gas to a perfect gas, that's OK with us engineers. But we'll stick with what we use.
I think you're misunderstanding what was said. Yes, engineers have used "Ideal Gas" as defined in the first post for many years. Engineers have also used the term "Perfect gas" to refer to something that fits all of the criteria for an ideal gas, plus has a constant Cv and Cp. Physicists call this an ideal gas (as opposed to the engineering ideal gas, where Cv and Cp can vary with temperature).

Mentor
I think you're misunderstanding what was said. Yes, engineers have used "Ideal Gas" as defined in the first post for many years. Engineers have also used the term "Perfect gas" to refer to something that fits all of the criteria for an ideal gas, plus has a constant Cv and Cp. Physicists call this an ideal gas (as opposed to the engineering ideal gas, where Cv and Cp can vary with temperature).

Oops. You're right. I did misinterpret.

DH: I owe you an apology. Sorry for my sarcastic comment. You were very gracious.
cjl: Thank you for clarifying this.

Chet

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