UNIVERSITY PHYSICS I CHAPTER 14 Kinetic theor Chapter 14 Kinetic theory The dynamics of article systems is called statistical mechanics The kinetic theory is a special aspect of the statistical mechanics of large number of particles Suitable averages of the physical characteristics and motions of individual particles provide information about the macroscopic behavior of the system as a whole
1 Chapter 14 Kinetic theory The kinetic theory is a special aspect of the statistical mechanics of large number of particles. Suitable averages of the physical characteristics and motions of individual particles provide information about the macroscopic behavior of the system as a whole. The dynamics of many-particle systems is called statistical mechanics
§14.1 The ideal gas 1. Newton's model of gas-static model The corpuscular particles of gas occupy fixed positions and filled the entire space between them Repel force F 1/r2→V个,Pc1/↓ 2. Kinetic model (Daniel Bernoulli, James Clerk Maxwell. Ludwig Boltzmann and others) Ogas is composed of many tiny particles, freely moving at high speed §14.1 The ideal gas @the pressure arises from the innumerable collisions of particles with each other and with the walls of the container. The pressure of a gas in thermal equilibrium inside a container never runs down or decreases with time the collisions must be modeled as completely elastic, the motion Is perpetua B The forces involved in the collisions of th particles of the gas with each other and with walls of the container must conservative briefly acting only during the intervals of the collisions and essentially zero otherwise
2 §14.1 The ideal gas 1. Newton’s model of gas—static model The corpuscular particles of gas occupy fixed positions and filled the entire space between them. Repel force F ∝ 1 r ⇒V ↑, P ∝ 1 V ↓ 2 2. Kinetic model (Daniel Bernoulli, James Clerk Maxwell, Ludwig Boltzmann and others) 1gas is composed of many tiny particles, freely moving at high speed. 2the pressure arises from the innumerable collisions of particles with each other and with the walls of the container. The pressure of a gas in thermal equilibrium inside a container never runs down or decreases with time, the collisions must be modeled as completely elastic, the motion is perpetual. 3 The forces involved in the collisions of the particles of the gas with each other and with walls of the container must conservative, briefly acting only during the intervals of the collisions and essentially zero otherwise. §14.1 The ideal gas
§14.1 The ideal gas o。。。。。 §14.1 The ideal gas @gases can be compressed easily. The space of the particles in gas is the order of 10 times larger than those of liquids and solids 3. Our purpose Find @the connection between temperature Tand pressure P and their microscopic essentials @the average velocity of the particles; specific heat-the microscopic essentials
3 §14.1 The ideal gas 4gases can be compressed easily. The space of the particles in gas is the order of 10 times larger than those of liquids and solids. 3. Our purpose Find: 1the connection between temperature T and pressure P and their microscopic essentials; 2the average velocity of the particles; 3specific heat—the microscopic essentials. §14.1 The ideal gas
§14.1 The ideal gas 4. The properties of ideal gas(model The ideal gas equation of state PV=nRT Othe number of particles N in the gas is very large for instance 10-2mol×6.02×1023/mol=6.02×101l 2NI particle <<y, the volume occupied by the particles themselves is a negligibly small fraction of the volume containing the gas. @all the particles are in random motion and obey Newtons law of motion §14.1 The ideal gas ④ the particles are ally likely to be moving in any direction--symmetry @the gas particles interact with each other and with the walls of the container only via elastic collisions. No force act on a particle except during a collision. all collisions elastic and of negligible duration @the gas is in thermal equilibrium with its surroundings Othe particles of the gas are identical and indistinguishable
4 4. The properties of ideal gas (model) The ideal gas equation of state: PV = nRT 2NVparticle<<V, the volume occupied by the particles themselves is a negligibly small fraction of the volume containing the gas. 1the number of particles N in the gas is very large, for instance 12 23 11 10 mol × 6.02×10 / mol = 6.02×10 − 3all the particles are in random motion and obey Newton’s law of motion. §14.1 The ideal gas 4the particles are equally likely to be moving in any direction--symmetry. 5the gas particles interact with each other and with the walls of the container only via elastic collisions. No force act on a particle except during a collision. All collisions elastic and of negligible duration. 6the gas is in thermal equilibrium with its surroundings. 7the particles of the gas are identical and indistinguishable. §14.1 The ideal gas
814. 2 the pressure and temperature of an ideal gas 1. The pressure of an ideal gas Othe probability that particles in element volume△ will collide Normal to with the wall 1A△L1△L1p△t P 2 AL L ② the change of the momentum of one particle Vibfr =viret mvi j+mvi k -mvi L t mvi)+ m 814.2 the pressure and temperature of an ideal gas Ap: = Piaft -Pi bft =-2mva i @the impulse given to the wall by the particles in the element volume Av F△t=-AD1=2mvai mmy 2 △t 2 Othe total impulse delivered to the wall during the interval At by all the particles that collide with the wall F△t △i=N〈v)A L L LT lotal number of particles
5 §14.2 the pressure and temperature of an ideal gas 1. The pressure of an ideal gas 1the probability that particles in element volume ∆V will collide with the wall L v t L L AL A L p x∆ = ∆ = ∆ = 2 1 2 1 2 1 2the change of the momentum of one particle i ˆ j ˆ m m v mv i mv j mv k v mv i mv j mv k ix iy iz ix iy iz ˆ ˆ ˆ ˆ ˆ ˆ i aft i bfr = − + + = + + r r ∆L A p p p mv i i ix ˆ 2 ∆ = i aft − i bft = − r r r 3the impulse given to the wall by the particles in the element volume ∆V ti L mv mv i L v t F t p mv i ix ix ix i i ix ˆ ˆ 2 2 ˆ 2 2 = ∆ ∆ ∆ = −∆ = r r 4the total impulse delivered to the wall during the interval ∆t by all the particles that collide with the wall N v ti L m v ti L m F t ix x i ˆ ˆ ( ) 2 2 ave∆ = ∑ ∆ = 〈 〉∆ r Total number of particles §14.2 the pressure and temperature of an ideal gas