Brownian Motion

1. Brownian motion is a model used to describe the movement of particles in a gas. This experiment can be used to observe Brownian Motion . If smoke is introduced into a small glass container and the container is illuminated and viewed through a microscope, the effect of molecular motion can be seen. This shows the path of a gas molecule. This can be described as a random walk. Brownian Motion The origin of pressure in gases mv Molecules are undergoing a change in momentum every second as they collide with the walls of the container. Change in momentum = -2mv Pressure is -mv The change in momentum divided by the time of the collision gives the force exerted. By Newton’s Third Law, the wall experiences a force and so a pressure.

2. Boyle’s Law = p If we combine Boyle’s Law with Charles’ law (V Boyle’s Law states that for a fixed mass of gas at a constant temperature, pressure is inversely proportional to the volume. Temperatures should be measured in Kelvin. The Kelvin scale is the absolute thermodynamic scale. At absolute zero, all substances have minimum internal energy. Ideal gases ‘Real’ gases tend to deviate form ideal behaviour at temperatures close to their boiling point. Ideal gases obey The Kinetic Theory of gases uses certain assumptions to show that, through the use of Newtonian mechanics, pressure is inversely proportional to volume and volume is directly proportional to thermodynamic temperature

3. Assumptions of the Kinetic Theory of Gases • A gas contains a large number of spherical particles • The forces between particles are negligible, except during collisions • Volume of particles is negligible compared to volume occupied by the gas • The time spent in collisions is negligible compared to the time between collisions • Collisions of particles with each other and with the container are perfectly elastic, so that no kinetic energy is lost. P is pressure; V is volume; T is temperature in Kelvin; n is number of moles; R is molar gas constant; N is number of molecules; k is the Boltzmann constant Ideal gas equations pV = nRT pV = NkT One mole of any substance is the amount of that substance that contains the same number of particles as there are carbon atoms in 0.012kg of carbon-12. One mole of any substance contains 6.02x1023 particles. This number is the Avogadro Constant, NA. The mean translational kinetic energy of a molecule is directly proportional to the absolute thermodynamic temperature. Energy of Ideal Gases mkt The internal energy of a gas is defined as the sum of the random distributions of kinetic and potential energies. When we’re looking at ideal gases, we say that the internal energy is equal to the kinetic energy alone (this is because an ideal gas has no attractive forces between molecules and so no potential energy.)