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13. Matter Very Simple
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Transcript of 13. Matter Very Simple
13. Matter Very SimpleYear 13
Learning Objectives Before the unit
I have learned
I have revised
I can show my understanding of effects, ideas and relationships by describing and explaining cases involving:
• The behaviour of ideal gases • The kinetic theory of ideal gases • Absolute (Kelvin) temperature as proportional to the average energy per particle, with average energy » kT as a useful approximation
• Energy transfer producing a change of temperature (in gases, liquids and solids) • Random walk of molecules in a gas; distance gone in N steps related to I can use the following words and phrases accurately when describing effects and observations:
• Absolute temperature • Ideal gas • Root mean square speed • Internal energy I can sketch, plot and interpret: • Graphs showing relationships between p, V and T for an ideal gas I can make calculations and estimates involving: • The universal gas law equation pV = NkT where N =nNA and Nk = nR ; number of moles n and Avogadro constant NA
• The equation for the kinetic model of a gas: • Temperature and energy change using ΔE = mcΔƟ
13. Matter Very Simple
Why does the balloon not expand?
www.phet.colorado.edu
Boyle’s Law
CpV
m = constantT = constant
pm = constantT = constant
VNCp
NCpV
/
No term for type of particle, therefore independent!
TV
m = constantp = constant
Tp
V = constantm = constant
The ideal gas law
NkTpVNTpV
NkTpV
measurable
unknown
NkTpV
NkTpV
The Gas Constant
6 x 1023 Avogadro Number, NA
9 MILES DEEP
Avogadro Number
• Number of particles in one mole of a substance
• E.g. 2 g of H2, 32 g of O2
Ideal gas law
nRTpVkNRkTnNpV
A
A
k
• NA was determined in 1909 so k could be calculated
• Determine k
particleper JK1038.1
mol10022.6molJK314.8
1-23
1-23
-1-1
k
NRkA
What does it mean?
Quick Check Questions
• Have a go at Q1-6 for Thursday
Pg 100 Q1
• Show that the pressure of an ideal gas doubles if its volume is halved
Vp
CNkTVNkTp
NkTpV
1
Pg 100 Q2
• A gas cylinder contains 100 litres of oxygen at room temperature and a pressure of 30 atm. Show that the cylinder can provide 6000 litres of oxygen at atmospheric pressure
2211
21
2
22
1
11
VpVpTT
TVp
TVp
NkTpV
NkTpV
litres 6000atm 1litres 200atm 30
2
2
2211
VV
VpVp
Pg 100 Q3
• A meteorological balloon has a volume of 2 m3 at ground level. Show that the designer should expect it to have a volume of 8 m3 at a height where the atmospheric pressure us 25 % of that at ground level, if the temperature remains the same.
2211
21
2
22
1
11
VpVpTT
TVp
TVp
NkTpV
NkTpV
32
23
21
2111
2211
m 8
m 24
441
V
V
VV
VpVp
VpVp
Pg 100 Q4
• In fact, in Q3 the temperature falls to -30 oC compared to 20 oC at ground level. Show that the designer should expect the balloon to have a volume of about 6.6 m3 at a height when the atmospheric pressure is 25 % of that at ground level.
2
22
1
11
TVp
TVp
NkTpV
NkTpV
32
3
2
23
2
1
m 6.6293
K243m 24293K243K
m 24
243293
VK
V
V
KTKT
Pg 100 Q5
• One mole of any ideal gas occupies a volume of about 22 litres at room temperature and pressure. Show that a small matchbox of air contains about 1020 molecules.
mol 000682.0
cm 15cm 22000
2
2
33
22
22
11
11
nn
RTnVp
RTnVpnRTpV
20
1-23
1-1-
10JK 1038.1
molJK 314.8mol 000682.0
N
N
knRN
nRNk
nRNkTpV
NkTpV
Pg 100 Q6
• 28 g of N2 contains 1 mole of molecules. Show that at a temperature of 546 K the nitrogen will occupy a volume of 22 litres at a pressure of 2 atm.
atmpKKatmp
TTpp
Tp
Tp
RTnVp
RTnVpnRTpV
2273
5461
2
2
1
212
2
2
1
1
22
22
11
11