# Chemistry - What's the difference between perfect and ideal gas?

## Solution 1:

An ideal gas is the same as a perfect gas. Just different naming. The usual name for such gases (for which is assumed that the particles that make up the gas have no interaction with each other) is ideal gas, perfect gas is what such a gas is named in Atkins physical chemistry book. Personally I like the perfect gas naming better as it illustrates the perfect nature of the assumptions made about it.

For the simple systems (like monoatomic gases) when we can assume a perfect/ideal gas, $C_{V,m}$ is independent of temperature. For real gases this is certainly not the case.

Note that $C_{V,m}=\frac{3}{2}R$ only holds for monoatomic gases.

## Solution 2:

Namely the result $C_V/n=\frac{3}{2}R$ is derived from a perfect gas and not an ideal gas and is only an approximation to the latter. Is this true?

So, let's look first at where $C_p-C_V=R$ comes from and then look at $C_V=\frac{3}{2}R$ to see what we find.

We start with the definition of heat capacity as being a change in energy per change in unit temperature,$$\Delta H=\int_{T_1}^{T_2}n\cdot C_p\,\mathrm dT$$ Now, I assume heat capacity to be independent of temperature

Then,$$\Delta H=n\cdot C_p(T_2-T_1)$$

Since $H=U+PV$ and pressure is held constant here, we rewrite the expression as $$\Delta U + P\Delta V=n\cdot C_p(T_2-T_1)$$ By the same integration performed above (but with $C_V$) we find that $\Delta U=n\cdot C_v(T_2-T_1)$ Combining those expressions and simplifying,

$$C_p-C_V=P\frac{\Delta V}{n\cdot\Delta T}$$

Using the ideal gas law, with constant pressure, we find,$$\frac{\Delta V}{\Delta T}=\frac{nR}{P}$$ Plugging that in, $$C_p-C_V=R$$

Now, for a monoatomic ideal gas, energy can only be stored in translation. Invoking the equipartition theorem to avoid having to do math and a little physics, we see that the energy of a monoatomic gas will be,$$U=\frac{3}{2}Nk_\mathrm bT$$ For $N=N_\mathrm A$ particles, we have, $$U=\frac{3}{2}RT$$

So, because $$C_V\equiv\left(\frac{\partial U}{\partial T}\right)_{P,n}$$ We see that, $$C_V=\frac{3}{2}R$$

Conclusions:

We see that in our derivation of the relationship $$C_p-C_V=R$$ we both used the ideal gas law and assumed heat capacity to be independent of temperature.

So, to answer the question quoted at the top of this answer, $\frac{C_V}{n}=\frac{3}{2}R$ is derived from the ideal gas, not the perfect gas.

And, in answer to the other question, our derivation required that we assume heat capacity to be constant with a change in temperature, so it was incorrect to say that heat is dependent on temperature for an ideal gas. It is true, however, that heat capacity varies with temperature for a real gas.

As to whether or not there is a difference between an ideal and perfect gas, I would look at that Wikipedia page posted in a comment above, but it seems superfluous to define something as a perfect gas when an ideal gas is already well understood and the perfect gas essentially behaves the same.

Hope that helps explain some of the math behind this.

## Solution 3:

As I recall P. W. Atkins etal point out that the interaction between particles in both ideal and perfect gases are constant (i.e. they don't vary with T or P). The difference is that for a percent gas the interactions are not only constant but they are equal to zero. For an ideal gas they just are constant.

Also, in regard to the comment made just above (The second point) should be that "The size of the particles is negligible when compared to the volume they occupy". In fact the distances are large in comparison and that is why the forces of attraction between particles are negligible.

## Solution 4:

Simply put, an ideal gas follows the ideal gas law. In thermodynamics and statistical mechanics, many physical relations are derived using the ideal gas law, sometimes accounting for Van der Waals forces or other non-negligible effects, depending on the conditions. The way I understand it, a perfect gas is an ideal gas, but is never treated as having non-interacting particles. I don't think the distinction is terribly important unless you plan on doing some thesis or dissertation in the fields of physical chemistry or condensed matter physics...