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13. Matter very simple. 13.2 The kinetic model. What’s the relationship. What’s the relationship. What temperature does water boil?. Using the ideal gas relationship. Answers. 0.103 m 3 0.11 m 3 7.14 litres
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13. Matter very simple 13.2 The kinetic model
What temperature does water boil?
Answers • 0.103 m3 • 0.11 m3 • 7.14 litres • If the lab is roughly 3 m high x 10 m x 10 m, volume = 300 m3, then about 12 kmol (with a mass of 360 kg) • 2.38 kg m–3 • 0.51 kg m–3
13. 2 The kinetic model • Modelling of the real world using simplifications • A gas is simply a collection of fast-moving, colliding particles, obeying the laws of mechanics
Ft +mv mv -2mv +2mv -mv
F Δt t
p y z x
Improve model: add particles mv mv mv mv
F t
Improve model: random directions mv mv mv mv
Improve model: random speeds mv mv mv mv
The ideal gas • For the model to work • Sample of gas must be large enough • Gas molecules are moving randomly in all directions with variable speeds • Collisions are elastic • Makes better predictions when: • Density of gas is low (space molecules take up is zero) • Energy of particles is large (no interactions)
The end of the clockwork Universe • Maxwell and Boltzmann were using Newtonian mechanics but in a new way Statistics
Energy in a gas We can determine the total internal energy of a monatomic gas just by knowing the pressure and volume, which are easy to measure!
Speed of a molecule • If you know the average kinetic energy then you can determine the average speed
Worked examples • If a particles follows a random walk of 10-7 m, and made 1010 steps. • What is the distance it has travelled? • What is the displacement?
The real stuff • Treating real gases as ideal is a simplification but a very useful one • This is what physics is, useful simplification!
Quick Check 1 • A ball of mass 0.2 kg travels at 2 ms-1 towards a ball and bounces back at the same speed. Show that it gives a momentum of 0.8 kg ms-1 to the wall
Quick Check 2 • Show that 20 mol of ideal gas contains 12 x 10^24 molecules.
Quick Check 3 • A mole of hydrogen occupies a volume of 0.024 m3 at a pressure of 105 Pa and a temperature of 300 K. Show that the mean kinetic energy of a hydrogen molecules is about 10-20 J.
Quick Check 4 • Show that the root mean square speed of H2 molecules (m = 3x10-27 kg) is about 2.6 kms -1. This is less than the escape velocity from the Earth, which is about 11 ms-1. Explain why hydrogen molecules do nethertheless escape from the atmosphere.
Quick Check 5 • Show that a typical molecule travelling at about 500 ms-1 will take only 20 ms to cross a room 10 m wide. Explain why a given molecule will actually take very much longer than this to travel only a few cm.
Quick check 6 • Show that in a mixture of oxygen (Mr = 32) and hydrogen (2) molecules the root mean square speeds of the two kinds of molecules will differ by a factor of four. Which is the fastest?