Thermal Physics Tutorial 2 - The Equation of State for an Ideal Gas

The Ideal Gas

We will be looking at gases and their behaviour under different conditions. The behaviour of ideal gases is quite easily predictable.  However real gases tend to behave slightly differently, especially those that consist of molecules.  So the ideal gas we will consider is:

There is no interaction between the molecules of an ideal gas except for collisions, which are always perfectly elastic. Helium is a good example of an ideal gas.

Question 1

Why is air not an ideal gas?



Ideal Gas Equation

There are three gas laws:

You are not expected to know them for the examination, but understanding them is useful.  Click HERE to find out more about the Gas Laws.

From the gas laws we can write:


The value of the constant depends on how much gas is being considered.  If we are looking at one mole of gas (which we will define later), then the constant is the universal molar gas constant. This is given the code R and has the value 8.31 J mol-1 K-1.

For n moles of a gas, we can write:


This is called the equation of state of an ideal gas. In this equation, SI units must be used, i.e. volume in m-3, pressure in Pa.  Temperature must be in Kelvin (K).  0 K = -273 oC.


The temperature quoted in degrees Celsius is commonly set as a bear trap.  Make sure you don't fall into it.

Question 2

What is the volume of 2 moles of helium atoms at a temperature of 20 oC and a pressure of 100 kPa?



A more useful version of the ideal gas equation is this:

p1V1 = p2V2

T1        T2

The term p1 stands for pressure in container 1 while p2 stands for pressure in container 2.

Question 3

A SCUBA* diver is deep underwater at a point where the pressure is 3.03 105 Pa, and the temperature is 10 oC.  The volume of her lungs is 3 litres.  She spots a dangerous animal and rises very rapidly to the surface where the temperature of the water is 20 oC and the air pressure is 1.01 105 Pa.  What is the volume of air in her lungs now?

*SCUBA stands for Self-Contained Underwater Breathing Apparatus.



The Mole

The mole is defined as:

 the same number of particles of a substance as there is in 12 g of 12C. 

This number is called the Avogadro constant, and is given the codes L or NA.

L = 6.02 x 1023 mol-1

The molar mass Mm is the mass of 1 mole of the substance.  Chemists quote this in grams per mole; for physics we need to convert to kilograms per mole by dividing by 1000 (or multiplying by 10-3).

Question 4

A sealed container of volume 0.8 10-3 m3 contains gas at a temperature of 320 K and a pressure of 1.5 106 Pa.  Calculate:

a)      The number of moles and molecules of the gas.                                     

b)      The mass of the gas if its molar mass is 32.0 10-3 kg                          

c)      The mass of a single molecule of gas.


An rule that is important for chemists is that equal numbers of moles occupy the same volume of space.  1 mole of any gas occupies 0.0224 m3 at Standard Temperature and Pressure (STP), where temperature is 273 K and pressure is 1.01 105 Pa.