General Physics 1 Hongqun Zhang The Department of Physics, Beijing Normal University June 2005

Chapter 13: Heat 13.1 Introduction 13.2 Ideal gas-A Macroscopic Description 13.3 Ideal gas-A Microscopic Description 13.4 Kinetic Calculation of Pressure 13.5 Kinetic Interpretation of Temperature

13.1 Introduction Heat is a branch of physics that is concerned with the analysis of thermal phenomena and thermal properties of matter. Macroscopic description Microscopic description

Macroscopic parameters: pressure (p), volume (V), temperature (T), internal energy (U), entropy (S) etc. Microscopic parameters: speeds, energies, masses, angular momenta, etc. Macroscopic description Thermodynamics Microscopic description Statistical Physics, Kinetic Theory

Thermodynamics Statistical Physics, Kinetic Theory Thermodynamics System: any limited macroscopic system that consists of a huge number of molecules or atoms. The Laws of Mechanics + Statistical Method All laws of thermodynamics are based on experiments.

13.2 Ideal gas-A Macroscopic Description Given a gas in a state of thermal equilibrium P, V, T For low enough values of the density, experiment shows that At constant T, pV=constant (Boyle ’ s Law) At constant p, V/T=constant (Law of Charles and Gay-Lussac)

Combined pV/T=constant Equation of State of Ideal Gas Where is the number of moles of gas, M is the mass of gas,  is the mass of one mole of gas, R is the universal gas constant, J/mol K. This relation is also the macroscopic definition of ideal gas.

13.3 Ideal gas-A Microscopic Description We assume: 1. The gas consists of a large number of identical particles (atoms or molecules). 1  m 3 water contains 3.3  molecules 2. The molecules are in random motion and obey Newton ’ s laws of motion. 3. The actual molecules take up a negligible small part of the volume occupied by the gas.

Vol. of gas can be changed over large range; vol. of liquid thousands times< vol. of gas. 4. No appreciable forces act on the molecules except during a collision. Molecular forces act over molecules size distances and molecule spacing >> size of molecule 5. Collision are elastic and of negligible duration. 6. The molecules moves in all directions with the same probability.

v ix dt x y dA (1) For one molecule 13.4 Kinetic Calculation of Pressure Impulse: (2) Dividing all molecules into groups according to their velocities as follows

Velocities Number of molecules Number per unit volume (3) For a group of molecules

(4) For all molecules Define the statistical average value of v 2 x for all molecules as follows

According to statistical assumption, where is average value of translational kinetic energy of one molecule. we have then

Discussion: (1) p is determined by n and, and is proportional to them. (2) It is a statistical law, not a mechanics law. Pressure formula of ideal gas

From We obtain in which is Boltzmann ’ s constant 13.5 Kinetic Interpretation of Temperature Avogadro law

By using of We finally get Discussion: (1) T is related to, it is the measurement of ; (2) It is also a statistical law, not a mechanics law. Temperature formula of ideal gas