Physical Chemistry Third Edition

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9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium PRINCIPAL FACTS AND IDEAS A model system that represe ...

384 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium 9.1 Macroscopic and Microscopic States of Macrosco ...

9.1 Macroscopic and Microscopic States of Macroscopic Systems 385 the total number of members of the set equal towi. The mean ca ...

386 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium Exercise 9.2 For the quiz scores in Exercise 9.1, ...

9.2 A Model System to Represent a Dilute Gas 387 The particles do not exert any forces on each other. The motions of the partic ...

388 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium and is the second time derivative of the position ...

9.2 A Model System to Represent a Dilute Gas 389 Exercise 9.3 Assume that a particle of massmmoves in thezdirection and is subje ...

390 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium The Microscopic States of Our Model System Accordi ...

9.2 A Model System to Represent a Dilute Gas 391 vz kvz ivx 0 ivx 1 jvy v 5 ivx 1 jvy 1 kvz kvz jvz vy vx Figure 9.4 A Velocity ...

392 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium c.The kinetic energy of a particle of massmis defi ...

9.2 A Model System to Represent a Dilute Gas 393 Exercise 9.6 Show that any constant can be added to a potential energy without ...

394 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium b. Construct a graph of the position of the partic ...

9.3 The Velocity Probability Distribution 395 Ifh(u) is a function ofu, its mean value is given by 〈h(u)〉 ∫u 2 u 1 h(u)f(u)du ( ...

396 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium We have assumed that the probability distribution ...

9.3 The Velocity Probability Distribution 397 Equation (9.3-14) is adifferential equation. Solving it means finding a functionft ...

398 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium Identification of the Parameterb We need some addi ...

9.3 The Velocity Probability Distribution 399 This must agree with the macroscopic energy of a dilute gas in Eq. (9.3-24), so th ...

400 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium EXAMPLE 9.3 Show that the Gaussian distribution of ...

9.3 The Velocity Probability Distribution 401 Solution <κx> 1 2 kBT 〈 κ^2 x 〉  (m 2 ) 2 〈 v^4 x 〉  (m 2 ) 2 ( m 2 πkBT ...