3.2c Kinetic energy and temperature

Kinetic energy and temperature

Temperature is defined as the average kinetic energy of the particles of a substance. For ideal gases we can derive an equation to directly relate these quantities using the Boltzmann constant (= 1.38064852 × 10^-23 JK^-1). This gives the AVERAGE kinetic energy increase per particle in an ideal gas when the temperature increase by one kelvin. It is important to remember that this is an average kinetic energy increase. In both ideal and real gases there will be a distribution of energies (the Maxwell-Boltzmann distribution) and in a real gas the velocities of the particles will depend on their masses - i.e. at the same temperature the average velocity of the particles in sample of hydrogen gas will be much higher than that of oxygen or nitrogen.

This difference of velocities helps to explain why hydrogen, the most common element in the universe, is not found in the Earth's atmosphere. The gas particle move so fast that in a relatively short amount of time any hydrogen will escape from the Earth into space. Earth's gravity is enough to hold on to gases such as oxygen, nitrogen and carbon dioxide, while other planets - such as Mars - are smaller and have lost a lot more of these heavier gases due to their weaker gravity.

The graph below shows speed distribution graphs for a number of gases of different masses, all at the same temperature of 298.15 K (25 °C). Not how the heavier gases have a much lower average velocity,