Kinetic theory & the behaviour of gases

1. Kinetic theory & the behaviour of gases Thursday 25th March

2. Learning outcomes use a particle model to describe solids, liquids, gases & changes of state explain gas pressure and thermal expansion in terms of kinetic theory describe how a barometer measures atmospheric pressure estimate the height of the atmosphere using a physical model recall and use the gas laws to make quantitative predictions relate the gas laws & Absolute Zero of temperature to the behaviour of ideal gases convert temperatures between Kelvin, Celsius and other scales introduce microscopic atoms and molecules through reasoning based on careful observation of macroscopic behaviour

3. How do we know? • What evidence is there for the existence of atoms?

4. Evidence for atoms crystals – regularity of surfaces, cleaving mixing different liquids change of volume: solid -> gas, liquid -> gas air occupies space and has mass diffusion: solid into solid, solid into liquid, gas into gas Brownian motion

5. All things are made of atoms “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? “I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms - little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. “In that sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.” Richard Feynman

6. Starting points - teaching challenges Atoms and molecules are far too small to be glimpsed by even the most highly-powered optical microscope. Diagrams of particle arrangements are often static. Dynamic animations showing the random thermal motion of particles, at all temperatures and in all states of matter, usefully overcome the misconceptions which static diagrams can foster. Students find it difficult to appreciate that gas pressure acts equally in all directions to account for the consequences of pressure differences to convert between units of volume (cm3, m3)

7. Starting points - mmisconceptions Students often think that particles have the properties of bulk matter (particles change in size as the temperature changes, particles can melt and solidify) have air in between them have thoughts and intentions e.g. ‘they prefer to move to places that are less crowded’. There is much confusion about the nature of particle motion in solids, liquids and gases.

8. Many states of matter superfluids, liquid crystals, solid solutions, plasmas, aerogels, foams, thin films, colloids, immiscible liquid mixtures, gas dissolved in a liquid, condensed matter, biopolymers….. … solid, liquid, gas

9. An ideal gas huge number of point molecules (occupy negligible volume) in continual random motion (and so ‘kinetic’) colliding elastically with each other and with container walls no forces between the molecules, except in collision time in collisions very small compared to time between collisions distance travelled between collisions (‘mean free path’) depends on gas density average speed of molecules depends on gas temperature in a gas composed of different molecules, the average molecular Ek is the same for all, so those with larger mass have smaller speed

10. Gases: bulk properties pressure = force applied over a unit area. SPT Forces, episode 8 Pressure

11. Gas pressure bombardment of the container walls change of momentum with each collision mv - (-mv) = 2mv

12. Deriving gas pressure relationship • Newton's Laws and Collisions • Applying Newton's Laws to an ideal gas under the assumptions of kinetic theory allows the determination of the average force on container walls. This treatment assumes that the collisions with the walls are perfectly elastic.

13. Under the assumptions of kinetic theory, the average force on container walls has been determined to be • The average force and pressure on a given wall depends only upon the components of velocity toward that wall. But it can be expressed in terms of the average of the entire translational kinetic energy using the assumption that the molecular motion is random. • and assuming random speeds in all directions • Then the pressure in a container can be expressed as • Expressed in terms of average molecular kinetic energy: • This leads to a concept of kinetic temperature and to the ideal gas law.

14. The expression for gas pressure developed from kinetic theory relates pressure and volume to the average molecular kinetic energy. Comparison with the ideal gas law leads to an expression for temperature sometimes referred to as the kinetic temperature. • This leads to the expression • The more familiar form expresses the average molecular kinetic energy: • It is important to note that the average kinetic energy used here is limited to the translational kinetic energy of the molecules. That is, they are treated as point masses and no account is made of internal degrees of freedom such as molecular rotation and vibration. This distinction becomes quite important when you deal with subjects like the specific heats of gases. When you try to assess specific heat, you must account for all the energy possessed by the molecules, and the temperature as ordinarily measured does not account for molecular rotation and vibration. The kinetic temperature is the variable needed for subjects like heat transfer, because it is the translational kinetic energy which leads to energy transfer from a hot area (larger kinetic temperature, higher molecular speeds) to a cold area (lower molecular speeds) in direct collisional transfer.

15. The speed of gas molecules Ways of estimating an average speed in air from the speed of sound (340 ms-1 at s.t.p.) thought experiment: a molecule falls freely from the top of the atmosphere Direct measurement: Zartman (1931) experiment to find the distribution of molecular speeds in a beam emitted from an oven opening. Average speedN2 at room temperature ~ 500 ms-1

16. The size of a molecule oil film experiment. Devised by John William Strutt, Lord Rayleigh, who also explained why the sky looks blue, and many other things! Nobel Prize-winner 1904.

17. The size of atoms ‘If an apple were magnified to the size of Earth, the atoms in it would each be about the size of a regular apple.’ Richard Feynman AFM showing atoms within hexagonal graphite unit cells. Image size 2 nm × 2 nm.

18. An empirical law Relationship between pressure and volume at constant temperature re-plot to show inverse proportionality Boyle’s law: pV = constant

19. Another Law –Extrapolating from data Relationship between temperature and volume at constant pressure Another empirical law… Charles’ law: In oC, a linear relationship. Direct proportionality if temperature scale is redefined. (mjp) T in kelvins, where K = oC - 273

20. Other gas laws pressure law: (T in kelvins) All 3 relationships combined: where n is number of moles, gas constant R = 8.31 J K-1 In a possibly more useful or meaningful form

21. Air pressure. Setting up a water barometer – well worth a go! http://www.youtube.com/watch?v=IRPvvJA8I_8 Or… http://www.rmets.org/weather/observing/make-barometer.php http://www.home-weather-stations-guide.com/make-your-own-barometer.html http://www.practicalphysics.org/go/Experiment_883.html

22. Height of the atmosphere weight of a column pressure of a column pressure of air and water columns are equal, so

23. Hydraulic machines Hydraulic machines exploit these facts: pressure is the same throughout a fluid (at same height). liquids are incompressible. How do hydraulic systems work?

24. Kinetic theory – a chronology c.420BC – atomic theory (Democritus: matter ultimately uncut-able) 1662 – Boyle’s law 1738 – Bernoulli Hydrodynamica (molecular collisions -> gas pressure) 1787 – Charles’ law 1798 – atomic theory of heat 1827 – Brownian motion 1834 – ideal gas law 1849 – kinetic theory k = 1.38 x 10-23 J K-1 (Boltzmann constant)

25. Gas properties PhET simulation Gas properties Pump gas molecules to a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.

26. Phase diagrams A phase diagram (p - T) shows boundaries between phases of matter. At the triple point, all 3 phases co-exist. Beyond the critical point, there is no distinction between gas and liquid phases. PhET: phase change simulation

27. Thermometer Scales Upper fixed point Lower fixed point Fundamental interval Linear, non linear, calibration and ranges