The Kinetic Theory of Gases Temperature as a measure of average kinetic energy of the particles

Objectives State the assumptions of the kinetic model of an ideal gas. State that temperature is a measure of the average random kinetic energy of the molecules of an ideal gas. Explain the macroscopic behavior of an ideal gas in terms of a molecular model. Write & understand the equation of state.

The Kinetic Theory of Gases The properties of gases can be understood in terms of a simple but effective mechanical model. The gas consists of a very large number of molecules moving randomly about with a range of speeds and colliding with each other and the container walls.

The Kinetic Theory of Gases We can make a model of this by making certain assumptions and seeing what these lead to. The basic assumptions of the kinetic theory of gases are: 1.A gas consists of a very large number of molecules. 2.Molecules moves with a range of speeds. 3.The volume of the molecules is negligible compared with the volume of the gas itself. 4.The collisions of the molecules with each other and the container walls are elastic (p and KE are conserved). 5.Molecules exert no forces on each other or the container except when in contact. 6.The duration of the collisions is very small compared with the time between collisions. 7.The molecules obey Newton’s Laws of Mechanics.

The Kinetic Theory of Gases

Example Four molecules have speeds of 300 m s -1, 350 m s -1, 380 m s -1, and 500 m s -1. Find the average speed and the root mean square speed.

Example If the root mean square molecular speed is doubled, what is the new temperature?

Molecular explanation of pressure The pressure of a gas originates from the collisions of the molecules with the walls of its container. At every collision, each molecule has its momentum changed, and so a force acts from the wall onto the molecule. By Newton’s Third Law, the molecule exerts an equal and opposite force on the wall. The total force due to all the colliding molecules, divided by the area over which the force acts gives the pressure of the gas.

Molecular explanation of pressure Pressure is the normal force per unit area. The pressure in a gas results from the collisions of the gas molecules with the walls of its container (and not from collisions between molecules).

Molecular explanation of pressure

Example A gas is compressed slowly by a piston. Explain why the temperature of the gas will stay the same.

Example A gas is compressed rapidly by a piston. Explain why the temperature of the gas will increase.

Example A gas expands isothermally. Explain from a molecular point of view why the pressure decreases.

The Equation of State A gas that obeys this law at all temperatures and pressures is said to be an ideal gas. Real gases obey this law only for a range of temperatures, pressures, and volumes.

Example A gas is heated at constant pressure. Explain why the volume must increase as well.

Example How many moles of gas are there in a gas of temperature 300 K, volume 0.02 m 3 and pressure 2 x 10 5 Pa?