# What is the difference between a perfect gas and an ideal gas?

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• Death eater
In summary, a perfect gas (or ideal gas) is a gas that follows the equation pV = nRT exactly under all conditions. While physicists use these terms interchangeably, engineers distinguish between them. In chemical engineering, an ideal gas is considered as the limiting behavior of a real gas at very low density, satisfying the ideal gas equation locally. The specific internal energy and enthalpy of an ideal gas only depend on temperature, while heat capacity, viscosity, and thermal conductivity are also functions of temperature. On the other hand, a perfect gas has a constant specific heat, while in an ideal gas it varies with temperature. From a kinetic theory perspective, an ideal gas is one where constituent particles have a shorter mean free path compared to the

#### Death eater

What is difference between perfect gas and ideal gas?

According to Atkins’ “Physical Chemistry”: A gas that obeys pV = nRT exactly under all conditions is called a perfect gas (or ideal gas).

There is a difference between usage in physics and in engineering. While physicists often use both terms interchangeably, this is not the case for engineers.

@Chestermiller can fill in the details better than me.

DrClaude said:
There is a difference between usage in physics and in engineering. While physicists often use both terms interchangeably, this is not the case for engineers.

@Chestermiller can fill in the details better than me.
I want to know about it used in engineering

In Chemical Engineering, we regard an ideal gas as the limiting behavior of a real gas at very low density. As such,

1. At thermodynamic equilibrium, ##pV=nRT##

2. In a system not at equilibrium (experiencing an irreversible process), the gas satisfies the ideal gas equation pv=RT locally, where v is the specific molar volume. The pressure, specific volume, and temperature may be varying with spatial position and time.

3. The specific internal energy and specific enthalpy are functions only of temperature (and approach those of the real gas at very low density)

4. The heat capacity at constant volume and the heat capacity at constant pressure are functions of temperature, but do not depend on pressure.

5. The viscosity and thermal conductivity are functions of temperature but not pressure.

6. The entropy includes the effect of temperature on heat capacity.

davenn, vanhees71 and berkeman
For a gas whose equation of state is exactly given by ##pV = nRT##, the specific internal energy depends only on temperature. Thus, if definition (1.) holds, definition (3.) is redundant.

Lord Jestocost said:
For a gas whose equation of state is exactly given by ##pV = nRT##, the specific internal energy depends only on temperature. Thus, if definition (1.) holds, definition (3.) is redundant.
Yes, that's correct. And I considered not including #3, but, for a neophyte to thermodynamics, I felt it would helpful to include.

Lord Jestocost
I haven't got the difference between ideal gas and perfect gas?

Death eater said:
I haven't got the difference between ideal gas and perfect gas?
We're still waiting for a Physicist to respond with their version of an ideal gas and perfect gas. We engineers use ideal gas and perfect gas interchangeably. Anyway, you said you were more interested in the engineering definition (which I gave).

Chestermiller said:
We're still waiting for a Physicist to respond with their version of an ideal gas and perfect gas. We engineers use ideal gas and perfect gas interchangeably. Anyway, you said you were more interested in the engineering definition (which I gave).
You have given the characterstics of ideal gas, they are true but I needed how can we differentiate between ideal and perfect gas?
I know one of the difference, it is that in ideal gases specific heat vary with temperature but in perfect gas specific heat is constant. I wanted to know more about it.

Death eater said:
You have given the characterstics of ideal gas, they are true but I needed how can we differentiate between ideal and perfect gas?
I know one of the difference, it is that in ideal gases specific heat vary with temperature but in perfect gas specific heat is constant. I wanted to know more about it.
Like I said, I'll leave it up to Physicists to provide their version of things. You have our answer from us engineers.

davenn
Indeed, at least in my community (relativistic heavy-ion physics, which uses relativistic statistical physics, including transport theory, thermal QFT, hydrodynamics, as one of its most important tools), there's no difference made between a "perfect" and an "ideal" gas. In fact, the expression "perfect gas" is never used.

From point of view of kinetic theory, one can define an ideal gas as a gas whose consituent particles have a mean free path which is much shorter than the typical space-time scales upon which the macroscopic properties of the gas changes. This implies equilibration (or relaxation) times much shorther than the typical timescales for changes of the macroscopic properties. Then the motion of the gas can be described well with ideal hydrodynamics, which implies that the gas is, on the resolution of macroscopic space-time scales, always in local thermal equilibrium.

vanhees71 said:
Indeed, at least in my community (relativistic heavy-ion physics, which uses relativistic statistical physics, including transport theory, thermal QFT, hydrodynamics, as one of its most important tools), there's no difference made between a "perfect" and an "ideal" gas. In fact, the expression "perfect gas" is never used.

From point of view of kinetic theory, one can define an ideal gas as a gas whose consituent particles have a mean free path which is much shorter than the typical space-time scales upon which the macroscopic properties of the gas changes. This implies equilibration (or relaxation) times much shorther than the typical timescales for changes of the macroscopic properties. Then the motion of the gas can be described well with ideal hydrodynamics, which implies that the gas is, on the resolution of macroscopic space-time scales, always in local thermal equilibrium.

I am confused after reading. I don't know what it is trying to say.

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vanhees71 said:
Indeed, at least in my community (relativistic heavy-ion physics, which uses relativistic statistical physics, including transport theory, thermal QFT, hydrodynamics, as one of its most important tools), there's no difference made between a "perfect" and an "ideal" gas. In fact, the expression "perfect gas" is never used.

From point of view of kinetic theory, one can define an ideal gas as a gas whose consituent particles have a mean free path which is much shorter than the typical space-time scales upon which the macroscopic properties of the gas changes. This implies equilibration (or relaxation) times much shorther than the typical timescales for changes of the macroscopic properties. Then the motion of the gas can be described well with ideal hydrodynamics, which implies that the gas is, on the resolution of macroscopic space-time scales, always in local thermal equilibrium.
Yikes. This is the same as what we engineers assume.

Death eater said:
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I am confused after reading. I don't know what it is trying to say.
According to the author your book, he defines a perfect gas as an ideal gas with constant heat capacity.

Chestermiller said:
According to the author your book, he defines a perfect gas as an ideal gas with constant heat capacity.
Now I am more confused. What is perfect gas?

Death eater said:
Now I am more confused. What is perfect gas?
I don't know how I can say this more precisely. Sorry. My advise is to not obsess over the difference, and to continue on with your learning.

vanhees71
Chestermiller said:
I don't know how I can say this more precisely. Sorry. My advise is to not obsess over the difference, and to continue on with your learning.
Ok, thanks any way for your tine

Death eater said:
Now I am more confused. What is perfect gas?

In Chapter III “SYSTEMS OF ONE COMPONENT” of the book “MODERN THERMODYNAMICS BY THE METHODS OF WILLARD GIBBS” by E. A. Guggenheim one finds:

Finally, let us consider a substance with the property that both its energy and its heat content are functions of the temperature only. A substance with this property is called a "perfect gas." For such a substance it then follows immediately from (21) [ H = E + PV ] that the product PV is a function of the temperature only, that is to say

for given T, PV = constant. (196-1)