CIE A Level Physics复习笔记15.2.1 Kinetic Theory of Gases

• Gases consist of atoms or molecules randomly moving around at high speeds
• The kinetic theory of gases models the thermodynamic behaviour of gases by linking the microscopic properties of particles (mass and speed) to macroscopic properties of particles (pressure and volume)

The theory is based on a set of the following assumptions:

• • Molecules of gas behave as identical, hard, perfectly elastic spheres
  • The volume of the molecules is negligible compared to the volume of the container
  • The time of a collision is negligible compared to the time between collisions
  • There are no forces of attraction or repulsion between the molecules
  • The molecules are in continuous random motion

• The number of molecules of gas in a container is very large, therefore the average behaviour (eg. speed) is usually considered

• The pressure of an ideal gas equation includes the mean square speed of the particles:

<c²>

• Where
  • c = average speed of the gas particles
  • <c²> has the units m² s^-2

• Since particles travel in all directions in 3D space and velocity is a vector, some particles will have a negative direction and others a positive direction
• When there are a large number of particles, the total positive and negative velocity values will cancel out, giving a net zero value overall
• In order to find the pressure of the gas, the velocities must be squared
  • This is a more useful method, since a negative or positive number squared is always positive
• To calculate the average speed of the particles in a gas, take the square root of the mean square speed:

• c_r.m.s is known as the root-mean-square speed and still has the units of m s^-1
• The mean square speed is not the same as the mean speed

Step 1:            Write out the equation for the pressure of an ideal gas with density

Step 2:            Rearrange for mean square speed

Step 3:            Substitute in values

Step 4:            To find the r.m.s value, take the square root of the mean square speed