lecture-ch19 - Contents 19 The kinetic theory of gases 1...

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Unformatted text preview: Contents 19 The kinetic theory of gases 1 19.1 Avogadro’s Number . . . . . . . . . . . . . . . . . . . . . . . . 1 19.2 Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 19.2.1 Work done by an ideal gas at constant temperature . . 3 19.2.2 Work done by an ideal gas at constant volume . . . . . 4 19.2.3 Work done by an ideal gas at constant pressure . . . . 4 19.3 Ideal Gas Pressure, Temperature and RMS Speed . . . . . . . 4 19.3.1 Translational kinetic energy . . . . . . . . . . . . . . . 6 19.4 Mean Free Path . . . . . . . . . . . . . . . . . . . . . . . . . . 6 19.5 The Distribution of Molecular Speeds . . . . . . . . . . . . . . 8 19.5.1 Average, RMS, and most probable speeds . . . . . . . 10 19.5.2 Optional: average relative speed . . . . . . . . . . . . . 12 19.6 The Molar Specific Heats of an Ideal Gas . . . . . . . . . . . . 13 19.6.1 Internal energy of an ideal gas . . . . . . . . . . . . . . 13 19.6.2 Molar specific heat C V at constant volume . . . . . . . 13 19.6.3 Molar specific heat C p at constant pressure . . . . . . . 14 19.7 Degrees of Freedom and Molar Specific Heats . . . . . . . . . 15 19.7.1 A Hint of Quantum Theory . . . . . . . . . . . . . . . 15 19.8 Adiabatic Expansion of an Ideal Gas . . . . . . . . . . . . . . 16 19.8.1 Free expansion . . . . . . . . . . . . . . . . . . . . . . 18 19 The kinetic theory of gases In this chapter we will introduce the kinetic theory of gases which relates the motion of the constituent atoms to the volume, pressure and temperature of the gas. The following topics will be covered: Ideal gas law. Internal energy of an ideal gas. Distribution of speeds among the atoms in a gas. Specific heat under constant volume. Specific heat under constant volume. Adiabatic expansion of an ideal gas. 19.1 Avogadro’s Number A mole of any substance is defined as the quantity contained in a mass equal to the molar mass of the substance. The mole of any substance contains the 1 same number of atoms (or molecules). This is known as: Avogadro ′ s number N A = 6 . 02 × 10 23 atoms/mole. The number n of moles in a mass M sample of a substance is given by the ratio: n = M sample M Here M is the molar mass of the substance. The number n = N N A Here N is the number of atoms in the mass M sample . The mass M sample = Nm. Here m is the mass of each molecule. 19.2 Ideal Gases It was found experimentally that 1 mole of any gas if placed in a containers that have the same volume V and kept at the same temperature T , ap- proximately all have the same pressure p . The small differences in pressure disappear if lower gas densities are used. Further experiments showed that all low density gases obey the equation: pV = nRT (ideal gas law) Here R = 8 . 31 J/mol · K and is known as the gas constant The equation itself is known as the ideal gas law. The constant R can be expressed as: R = kN A Here k is called the Boltzmann constant and it is equal to 1 . 38 × 10- 23 J/K ....
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lecture-ch19 - Contents 19 The kinetic theory of gases 1...

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