Presentation on theme: "The Kinetic Theory of Gases"— Presentation transcript:
1 The Kinetic Theory of Gases Chapter 21The Kinetic Theory of Gases
2 Ideal gases The gas under consideration is a pure substance All molecules are identicalMacroscopic properties of a gas: P, V, TThe number of molecules in the gas is large, and the average separation between the molecules is large compared with their dimensions – the molecules occupy a negligible volume within the containerThe molecules obey Newton’s laws of motion, but as a whole they move randomly (any molecule can move in any direction with any speed)
3 Ideal gasesThe molecules interact only by short-range forces during elastic collisionsThe molecules make elastic collisions with the walls and these collisions lead to the macroscopic pressure on the walls of the containerAt low pressures the behavior of molecular gases approximate that of ideal gases quite well
6 Translational kinetic energy Average translational kinetic energy:At a given temperature, ideal gas molecules have the same average translational kinetic energyTemperature is proportional to the average translational kinetic energy of a gas
7 Internal energy For the sample of n moles, the internal energy: Internal energy of an ideal gas is a function of gas temperature only
8 Work done by an ideal gas at constant temperature Isothermal process – a process at a constant temperatureWork (isothermal expansion)
9 Work done by an ideal gas at constant volume and constant pressure Isovolumetric process – a process at a constant volumeIsobaric process – a process at a constant pressure
10 Molar specific heat at constant volume Heat related to temperature change:Internal energy change:
11 Molar specific heat at constant pressure Heat related to temperature change:Internal energy change:
15 Degrees of freedom and molar specific heat 3 translations, 3 rotations, + oscillations
16 Degrees of freedom and molar specific heat 3 translations, 3 rotations, + oscillationsIn polyatomic molecules differentdegrees of freedom contribute atdifferent temperatures
17 Chapter 21Problem 13A 1.00-mol sample of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate (a) the energy transferred to the gas by heat, (b) the increase in its internal energy, and (c) the work done on the gas.
18 Chapter 21Problem 27Consider 2.00 mol of an ideal diatomic gas. (a) Find the total heat capacity at constant volume and the total heat capacity at constant pressure, assuming the molecules rotate but do not vibrate (b) Repeat part (a), assuming the molecules both rotate and vibrate.
19 Distribution of molecular speeds Not all the molecules have the same speedMaxwell’s speed distribution law:Nvdv – fraction of molecules with speeds in the range from v to v + dvJames Clerk Maxwell( )
20 Distribution of molecular speeds Distribution function is normalized to 1:Average speed:RMS speed:Most probablespeed:
21 Chapter 21Problem 44As a 1.00-mol sample of a monatomic ideal gas expands adiabatically, the work done on it is – 2500 J. The initial temperature and pressure of the gas are 500 K and 3.60 atm. Calculate (a) the final temperature and (b) the final pressure.