13. matter very simple
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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 - PowerPoint PPT PresentationTRANSCRIPT
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13. Matter very simple13.2 The kinetic model
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What’s the relationshipGas Law Equation
Boyle’s Law
Charles’ Law
Pressure Law
Amount Law
Ideal Gas Law
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What’s the relationshipGas Law Equation
Boyle’s Law
Charles’ Law
Pressure Law
Amount Law
Ideal Gas Law
Vp 1
TV
Tp
Np
nRTpV
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Vp 1
What temperature does water boil?
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TV
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Tp
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Np
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nRTpV
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Using the ideal gas relationship
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Answers
1. 0.103 m3
2. 0.11 m3
3. 7.14 litres4. 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)
5. 2.38 kg m–3
6. 0.51 kg m–3
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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
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mv
xv
t
vxt
vst
tsv
21
2
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mv Ft
+mv-mv-2mv +2mv
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tmvF
xmvF
vxmvF
2
/22
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F
t
Δt
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x
y
z
xyzV
p
yzA
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Calculating pressure
Vmvp
xyzmvp
AFp
yzAxmvF
wall
wall
2
2
2
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mv
mv
mv
mv
Improve model: add particles
VNmvp
2
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F
t
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mv
mv mv
mv
Improve model: random directions
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F
t
1/3 as many collision
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VNmvp
2
31
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mv
mv mv
mv
Improve model: random speeds
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F
t
1/3 as many collision
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VvNmp2
31
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VvNmp2
31
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VvNmp2
31
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VvNmp2
31
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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)
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The end of the clockwork Universe
• Maxwell and Boltzmann were using Newtonian mechanics but in a new way
Statistics
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Temperature and Energy
kTvm
kTvm
NkTvNm
vNmpV
NkTpV
232
21
2
231
231
3
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Temperature and Energy
RTUkNR
kTNvmN
NkTvNm
kTvm
A
AA
23
232
21
232
21
2 3
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Energy in a gas
pVNkTvNmU 23
232
21
We can determine the total internal energy of a monatomic gas just by knowing the pressure and volume, which are easy to measure!
2O 2H 2N
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Speed of a molecule
• If you know the average kinetic energy then you can determine the average speed
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Seeing primordial living motion
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Let’s flip a coin
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How far will a molecule go after N steps?
N
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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?
md 10001010 710
ms 01.01010 710
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The real stuff
• Treating real gases as ideal is a simplification but a very useful one
• This is what physics is, useful simplification!
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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
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Quick Check 2
• Show that 20 mol of ideal gas contains 12 x 10^24 molecules.
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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.
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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.
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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.
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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?