Ideal gases IB DP Physics Study Notes - 2025 Syllabus

Ideal gases IB DP Physics Study Notes

Ideal gases IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

that ideal gases are described in terms of the kinetic theory and constitute a modelled system used to approximate the behaviour of real gases
that the ideal gas law equation can be derived from the empirical gas laws for constant pressure, constant volume and constant temperature as given by $\frac{P V}{T}=$ constant
the equations governing the behaviour of ideal gases as given by $P V=N k_{\mathrm{B}} T$ and $P V=n R T$

Standard level and higher level: 6 hours
Additional higher level: There is no additional higher level content

IB DP Physics 2025 -Study Notes -All Topics

The kinetic model of an ideal gas

An ideal gas is an imaginary gas that is used to model real gases, and has the following properties
Just as temperature was a measure of the random kinetic energy of molecules for solids and liquids, so it is for an ideal gas.
If the temperature of a gas increases, so does the average speed (and hence kinetic energy) of the molecules.
Looking at this animation again we can see that if the speed of the molecules increases, then the number of collisions with the container walls will also increase.
Thus the pressure will increase if the temperature increases.
Consider small, medium and large containers.
In a smaller volume the molecules have less distance to travel to hit a wall. Thus the wall is hit more often.
Thus the pressure will be bigger if the volume is smaller.
Consider a syringe full of an ideal gas.
If we make the volume less we see that the temperature will increase.
Since the plunger exerts a force on the gas, and executes a displacement, it does work on the gas.
From the work-kinetic energy theorem we know that if we do work on the gas, its kinetic energy must increase.
Thus its speed will increase, which means its temperature increases.
On the other hand, if the process is reversed the gas will do the work, lose E_K and cool.

The temperature of an ideal gas is reduced. Which one of the following statements is true?

A. The molecules collide with the walls of the container less frequently.
B. The molecules collide with each other more frequently.
C. The time of contact between the molecules and the wall is reduced.
D. The time of contact between molecules is increased.

▶️Answer/Explanation

Solution:

Ans:A

Temperature is a measure of the $E_K$ of the gas.

Reducing the $E_K$ reduces the frequency of collisions.

For perfectly elastic collisions (as in an ideal gas) contact time is zero regardless of $E_K$.

Equation of state for an ideal gas

Without proof, here is the equation of state for an ideal gas.
We will explain what an ideal gas is a bit later…
The variables p (pressure), V (volume), n (number of moles), and T (temperature) are all called the four state variables.
p is measured in Pascals or Nm^-2.
V is measured in m3.
T is measured in K.

Differences between real and ideal gases

Recall the properties of an ideal gas:
The kinetic theory of gases is, of course, a model.
As such, it doesn’t apply perfectly to real gases.
Here are the properties of a real gas.

FYI

Real gases are often polyatomic (N₂, O₂, H₂O, NH4, etc.) and thus not spherical.
Ideal gases cannot be liquefied, but real gases have intermolecular forces and non-zero volume, so they can be liquefied.

The equation of state for an ideal gas, $p V=n R T$, describes the behaviour of real gases

A. only at low pressures and large volumes.
B. only at high temperatures.
C. only at large volumes and large pressures.
D. at all pressures and volumes.

▶️Answer/Explanation

Solution:

Ans:A

Under high pressure or low volume real gases’ intermolecular forces come into play.
Under low pressure or large volume real gases’ obey the equation of state.

Ideal gases IB DP Physics Study Notes

Ideal gases IB DP Physics Study Notes - 2025 Syllabus