![]() If the walls are cooler than the gas, they will get warmer, returning less kinetic energy to the gas, and causing it to cool until thermal equilibrium is reached. The magnitude of the velocity of each molecule is indicated by the length of the arrow. Figure 5.6.2: A microscopic picture of the molecules in a gas (balls) as a specific time. Collisions with the walls of the container will transfer more momentum, and thus more kinetic energy, to the walls. \(v\) is the magnitude of the velocity of a molecule.Īs the temperature of a gas rises, the average velocity of the molecules will increase a doubling of the temperature will increase this velocity by a factor of four.\(KE\) is the kinetic energy of a molecule,.Kinetic energy is the energy a body has by virtue of its motion: Kinetic Interpretation of Absolute TemperatureĪccording to the kinetic molecular theory, the average kinetic energy of an ideal gas is directly proportional to the absolute temperature. The "hardness" of the impact of the molecules with the wall will be related to the velocity of the molecules times the mass of the molecules.The magnitude of the pressure is related to how hard and how often the molecules strike the wall.The pressure of a gas is causes by collisions of the molecules with the walls of the container.With a force, \(F\), that is exerted on the surface of area \(A\) exerting a pressure This change in velocity Δ V is equivalent to a n acceleration \(a\) according to Newton's second law, Since the collisions are elastic, the molecule bounces back with the same velocity in the opposite direction. Figure 5.6.1: Pressure arises from the force due to the acceleration of molecules as they bound off a container's wallsĪt each collision, a molecule moving with momentum mv strikes the surface. Any surface in contact with the gas is constantly bombarded by the molecules. The kinetic molecular theory makes it easy to see why a gas should exert a pressure on the walls of a container. If gases do in fact consist of widely-separated particles, then the observable properties of gases must be explainable in terms of the simple mechanics that govern the motions of the individual molecules. This implies that all molecular motion would cease if the temperature were reduced to absolute zero. Notice that the term “average” is very important here the velocities and kinetic energies of individual molecules will span a wide range of values, and some will even have zero velocity at a given instant. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature.Collisions are perfectly elastic when two molecules collide, they change their directions and kinetic energies, but the total kinetic energy is conserved.This means that the molecules move in straight lines (see demo illustration at the left) until they collide with each other or with the walls of the container. ![]() The molecules are in constant random motion, and as material bodies, they obey Newton's laws of motion.The molecules of an ideal gas exert no attractive forces on each other, or on the walls of the container.The volume occupied by the molecules of the gas is negligible compared to the volume of the gas itself. A gas is composed of molecules that are separated by average distances that are much greater than the sizes of the molecules themselves.The five basic tenets of the kinetic-molecular theory are as follows: Gas molecules are in rapid and continuous motion at ordinary temperatures and pressures their velocities are of the order of 0.1-1 km/sec and each molecule experiences approximately 10 10collisions with other molecules every second. According to this model, most of the volume occupied by a gas is empty space this is the main feature that distinguishes gases from condensed states of matter (liquids and solids) in which neighboring molecules are constantly in contact. This fundamental assumption of the kinetic-molecular model helps us understand a wide range of commonly-observed phenomena. The molecules of a gas are in a state of perpetual motion in which the velocity (that is, the speed and direction) of each molecule is completely random and independent of that of the other molecules. The Fundamentals of Kinetic Molecular Theory (KMT)
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