kinetic theory of gas气体动力学理论kinetic theory of gas气体动力学理论.pdf

Chapter 16 Kinetic Theory of Gases 16-1 The Ideal Gas Law and the Molecular Interpretation of Temperature 16-2 Distribution of Molecular Speeds 16-6 Mean Free Path 16-1 The Ideal Gas Law and the Molecular Interpretation of Temperature Our first model of a many-particle system: the Ideal Gas Models of matter: gas models (random motion of particles) Air at normal conditions: ~ 2.7×1019 molecules in 1 cm3 of air Size of the molecules ~ (2-3) × 10-10 m, Distance between the molecules ~ 3 × 10-9 m The average speed - 500 m/s The mean free path - 10-7 m (0.1 micron) The number of collisions in 1 second - 5 × 109 1. The ideal gas model 1) Assumptions about the molecules in an ideal gas The ideal gas model - works well at low densities (diluted gases) • all the molecules are identical, N is huge; • the molecules are tiny compared to their average separation (point masses); • the molecules do not interact with each other; • the molecules obey Newton’s laws of motion, their motion is random; • collisions between the molecules and the container walls are elastic. 2) Statistical assumptions about an ideal gas In an equilibrium state, the distribution of molecules on the position is uniform, which means that the density of number of molecules is the same everywhere, dN N n d V V Velocities of molecules are different. Each molecule has its velocity, which may be changed due to collisions. In an equilibrium state, velocity of each molecule has the same probability to point to any directions. That is, the distribution of velocity of molecules is uniform in direction, which leads to the mean-square speeds of all components of velocity are same. Let v2 be the average value of vx2