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The final mock (Physics) > Unit 3.3 Kinetic Theory (Derivation Gamble) > Flashcards

Unit 3.3 Kinetic Theory (Derivation Gamble) Flashcards

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1
Q

Summarise the main ideas about particles in a solid
(6 things)

A
  • Regular pattern
  • Fixed shape & volume
  • Particles vibrate in place, low kinetic energy
  • No space between particles
  • Intermolecular forces = strong,
  • they have low potential energy
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2
Q

Summarise the main ideas about particles in a liquid
(7 things)

A
  • No regular pattern
  • No fixed shape & volume
  • Particles move around each other, med. kinetic energy
  • There’s space between particles,
  • but are touching
  • Intermolecular forces = medium.
  • ∴ medium potential energy
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3
Q

Summarise the main ideas about particles in a gas
(5 things)

A
  • No regular pattern/fixed shape/volume
  • Particles move fast & free, has high kinetic energy
  • Space between particles
  • Intermolecular forces are weak [zero],
  • they have high potential energy
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4
Q

Define the internal energy (U) of a system?
(3 parts)

A
  • The sum of the random distributions
  • of kinetic and potential energies
  • of all the molecules in the system
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5
Q

What is an ideal gas?
(2 parts)

A
  • Gas that strictly obeys the equation of state:
  • Pv = nRT
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6
Q

What is the ideal gas equation?
(In data booklet)

A

Pv = nRT

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7
Q

Ideal gas equation in word form?

A

Pressure x Volume = moles x molar gas constant x temperature

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8
Q

Define P
(ideal gas equation)

A

Pressure
(Pa)

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9
Q

Define v
(ideal gas equation)

A

Volume
(m3)

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10
Q

Define n
(ideal gas equation)

A

Moles
(mol)

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11
Q

Define r
(ideal gas equation) Data booklet

A

Molar gas constant = 8.31
(J Mol-1 K-1)

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12
Q

Define T
(ideal gas equation)

A

Kelvins
(K)

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13
Q

How does an ideal gas “strictly” obeys the equation of state PV=nRT?
(3 things)

A

Must have:
- Negligible vol. of molecules
- Elastic collisions
- No intermolecular forces

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14
Q

Features of an ideal gas?
(2 things)

A
  • No molecular force
  • Simply be kinetic energy
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15
Q

Charles law & Boyles law proofs?

A

Take action if needed
(If u see a question on it, then…)

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16
Q

What is meant by temperature?
(2-way)

A
  • A measure of avg. kinetic energy
  • of the particles in a substance
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17
Q

Define absolute zero?
(2-way)

A
  • The temperature of a system when
  • it has MINIMUM internal energy
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18
Q

How do u find the value for absolute zero in a graph?
(Refer to page 9 otherwise…)
(3-way)

A
  • rise/run = gradient
  • V = mx + c, 0 = mx + c
  • -c/m = absolute zero
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19
Q

How to convert Celsius to Kelvins?
(In data booklet kinda)

A

Add 273.15

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20
Q

How to convert Kelvins to Celsius?
(In data booklet kinda)

A

Minus 273.15

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21
Q

What are the 3 gas laws?

A
  • Boyle’s law
  • Charles’ law
  • Pressure law
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22
Q

How can the gas laws only be applied?

A

For a fixed mass of gas
(n = constant)

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23
Q

Define isothermal

A

When the temperature is constant

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24
Q

Define isobaric

A

When the pressure is constant

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25
Q

Define isochoric

A

When the volume is constant

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26
Q

What is Boyle’s law?
(Gas laws, 2 each)

A
  • PV = constant
  • P1V1 = P2V2
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27
Q

What is Charles’ law?
(Gas laws, 2 each)

A
  • V/T = constant
  • V1/T1 = V2/T2
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28
Q

What is the Pressure law?
(Gas laws, 2 each)

A
  • P/T = constant
  • P1/T1 = P2/T2
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29
Q

Which gas law is isothermal?

A

Boyle’s law
P1V1 = P2V2

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30
Q

Which gas law is isobaric?

A

Charles’ law
V1/T1 = V2/T2

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31
Q

Which gas law is isochoric?

A

Pressure law
P1/T1 = P2/T2

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32
Q

What equation do u get for combining all 3 gas laws?

A

P1V1/T1 = P2V2/T2

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33
Q

Equation to gain pressure?

A

Pa = N/m3

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34
Q

Pressure equation in word form?

A

Pressure = force/volume

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35
Q

1Pa = ?

A

1Nm-3

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36
Q

Define 1 mole?
(2-way)

A
  • The n° of atoms
  • in 12g of carbon-12
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37
Q

What is Avagadro’s constant?
(in data booklet)

A

6.02 x 1023
(Na)

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38
Q

What is molar mass?

A

Mass of one mole

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39
Q

Define molar mass?
(2-way)

A
  • Amount of a substance that
  • contains 6.02 x 1023 particles
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40
Q

But what actually is molar mass?
(Symbol typa thingy)

A

Mr
(Relative molecular mass)

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41
Q

How to calculate n° of moles in a given mass of any gas?
(In data booklet)

A

n = m/M

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42
Q

Word form of n° of mols equation?

A

Number of moles = mass of gas/Molar mass

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43
Q

Define mass of gas?
(Mols equation)

A

Grams
(g)

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44
Q

Define relative molecular mass (Mr)
(2-way)

A
  • The sum of all the relative atomic masses
  • for all the atoms in a given formula
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45
Q

The equation to prove Mr is related to M?
(In data booklet)

A

M(kg) = Mr/1000

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46
Q

Word form of M equation

A

Molar mass (kg) = Relative molecular mass/1000

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47
Q

What are the 3 things that define a “real gas”?

A
  • Particles have volume
  • Energy lost in collisions
  • Intermolecular forces
48
Q

What is the equation linking with the n° of molecules it contains?
(In data booklet)

A

PV = NkT

49
Q

Word form of equation linking with n° of molecules it contains?

A

Pressure x Volume = N° of molecules x Boltzmann’s constant x Temperature

50
Q

Define P
(2nd ideal gas equation)

A

Pressure
(Pa)

51
Q

Define V
(2nd ideal gas equation)

A

Volume of gas
(m3)

52
Q

Define N
(2nd ideal gas equation)

A

Number of molecules

53
Q

Define k
(2nd ideal gas equation)

A

Boltzmann’s constant
(1.38 x 10-23JK-1, in data booklet)

54
Q

However, how is Boltzmann’s constant gained?
(PV = NkT)
(4-way… whiteboard)

A
  • PV = nRT, n = N/NA
  • PV = (N/NA)RT
  • k = R/NA
  • HENCE, PV = NkT
55
Q

Describe how smoke particles move?
(3 points)

A
  • Jerky motion
  • Random direction
  • Various speeds
56
Q

Explain why smoke particles move like that?
(5 points)

A
  • Random collisions between smoke PTCL & air PTCL
  • Each collision = change of momentum
  • Due to Newton’s 2nd law, force is applied
  • If smoke PTCL’s bombarded with enough air PTCL’s,
  • force can change smoke PTCL’s speed & direction
57
Q

Why do gas particles exert a pressure on their container?
(6 points)

A
  • Random collisions between gas PTCL’s and container walls
  • = change of momentum for the particles
  • Means the wall must’ve applied a force on particles
  • Due to Newton’s 3rd law,
  • particles must exert equal & opposite force on wall
  • Force provides pressure as Pa = N/m3
58
Q

How do u explain the gas laws
(3 steps)

A
  1. State what stays the same
  2. State changes and effect it has on rate of collisions
  3. Link to force and so pressure
59
Q

Explain why P ∝ 1/V at constant temperature
(Boyle’s Law)
(2 points + 3-way + 1)

A
  • Constant temperature
  • Decreased volume
  • Each collision provides force
  • Force increases
  • Therefore more pressure
  • As volume decreases, pressure increases
60
Q

Explain in detail constant temperature?
(Boyle’s Law)
(2 points)

A
  • KE constant
  • Speed constant
61
Q

Explain in detail decreased volume?
(Boyle’s Law)
(2 points)

A
  • Less distance between collision with wall
  • More collisions per second
62
Q

Explain why P ∝ T at constant volume
(Pressure Law)
(2 points, 3-way + 1)

A
  • Constant volume
  • Increased temperature
  • Same distance but increased speed
  • More collisions per second
  • Increased rate of collisions
  • As pressure increases, temperature increases
63
Q

Explain in detail constant volume?
(Pressure law)
(2 points)

A
  • Constant distance between collision w/ wall
  • Constant collisions per second
64
Q

Explain in detail increased temperature?
(Pressure law)
(2 points)

A
  • Increased KE
  • Mean speed increases
65
Q

Explain why V ∝ T at constant pressure
(Charles’ Law)
(2 points, 3-way + 1)

A
  • Constant pressure
  • Increased temperature
  • To maintain pressure (rate of collisions)
  • distance between walls increases
  • Volume increases
  • As volume increases, temperature increases at constant pressure
66
Q

Explain in detail constant pressure?
(Charles’ Law)
(2 points)

A
  • Constant force
  • Rate of collisions constant
67
Q

Explain in detail increased temperature?
(Charles’ Law)
(2 points-1way)

A
  • Increased speed of particles
  • Increase rate of particles (rate of change of momentum)
  • Unless distance between collisions increase
68
Q

All the particles in an ideal gas, tell me about their speed?
(1 + 2-way)

A
  • They don’t move at identical speeds
  • Distribution of energy between particles
  • = random
69
Q

3 ways they define the types of speed of a particle in an ideal gas?

A
  • Most probable speed
  • Mean speed
  • Root mean square speed
70
Q

Define most probable speed?
(2 points)

A
  • Most particles move at this speed
  • Peak of Maxwell-Boltzmann distribution
71
Q

Define mean speed?
(what.)

A

Average value of all speeds

72
Q

Formula to find mean speed?
(C̅)
Not in data booklet

A

C̅ = sum of all particles/n° of particles

73
Q

Define root mean square speed?
(rms)
(2-way)

A
  • The square root of
  • the mean square speed of the molecules
74
Q

Formula to find rms speed?
Not in data booklet

A

√C̅2 = √(sum of all speeds/n° of particles)

75
Q

What are 3 simplifying assumptions to be made before deriving the “kinetic theory equation”?
(Ideal gas…)

A
  • No intermolecular forces
  • Negligible volume of molecules
  • Elastic collisions between molecules
76
Q

Another “go-to” way of certain simplifying assumptions?
(“THE”, kinetic theory equation)

A

DELVE

77
Q

Define D
(2-way)
(DELVE)

A
  • Duration of collisions very short
  • compared to time between collisions
78
Q

Define E
(DELVE)

A

Energy distribution for particles is random

79
Q

Define L
(DELVE)

A

Large n° of particles; large n° of collisions

80
Q

Define V
(DELVE)

A

Velocity of particles is uniform between collisions

81
Q

Define E… 2nd one
(2-way)
(DELVE)

A
  • Even distribution of particle motion
  • in all directions
82
Q

What’s the equation for the pressure of a [real] gas?
(NOT IN DATA BOOKLET)

A

pV = ⅓NmC̅2

83
Q

Define P
(pressure of a gas)

A

Pressure
(Nm-2)

84
Q

Define V
(pressure of a gas)

A

Volume
(m3)

85
Q

Define m
(pressure of a gas)

A

Mass/one particle
(kg)

86
Q

Define N
(pressure of a gas)

A

N° of molecules

87
Q

Define C̅2
(pressure of a gas)

A

Mean square speed
(m2s-2??)

88
Q

How is pressure provided?
(3 things)
(pressure of a gas)

A
  • Newton’s 3rd law
  • Force of molecules
  • colliding with the container
89
Q

What does the force depend on?
(3 things)
(pressure of a gas)

A
  • Newton’s 2nd law
  • Depends on the change of momentum
  • of particles due to collisions
90
Q

How many stages are there to the derivation of the equation for the pressure of a gas?
(A whiteboard, is op)

A

About 9 stages
(my way)

91
Q

Tell me stage 1 of the derivation of the equation for the pressure of a gas?
(5 steps… perhaps I’ll only learn these)

A
  • Molecules move in all directions
  • 1 molecule of mass (m)
  • Travels with velocity (cx)
  • Collides with walls of container
  • Each wall has a length of L
92
Q

Tell me stage 2 of the derivation of the equation for the pressure of a gas?
(5 steps…. just that equation)

A
  • Calculate the change in momentum
  • Before it moves with velocity vx
  • and after the collision it moves with -vx
  • △mcx = (mcx) - (-mcx) -> △mcx = 2mcx
  • Equation 1
93
Q

Tell me stage 3 of the derivation of the equation for the pressure of a gas?
(6 steps… just that equation)

A
  • Time given by distance/speed
  • Speed is cx
  • Distance is twice the length of box
  • (distance to collide, then collide again with same wall)
  • t = 2L/cx
  • Equation 2
94
Q

Tell me stage 4 of the derivation of the equation for the pressure of a gas?
(5 steps… just that equation)

A
  • Calculate force by:
  • Force = change in momentum/time
  • Sub in equation 1 & 2
  • F = 2mcx/2L/cx -> mc2x/L
  • Equation 3
95
Q

Tell me stage 5 of the derivation of the equation for the pressure of a gas?
(6 steps… just that equation)

A
  • Equation 3 gives force of one molecule
  • acting on the side of the container
  • Can now calculate pressure one molecule causes in x direction
  • p = F/A, sub in equation 3
  • p = mc2x/2L/cx -> mc2x/L3
  • Equation 3.5
96
Q

Tell me stage 6 of the derivation of the equation for the pressure of a gas?
(5 steps… just that equation)

A
  • Assume box is a cube
  • Can replace L3 with V (equation 3.5)
  • Both units are m3
  • p = mc2x/V
  • Equation 4
97
Q

What’s the jig of equation 4? [stage 6]
(Derivation of the equation for the pressure of a gas)
(2-way… meh sure why not)

A
  • Gives pressure of one molecule
  • acting on the side of the container in 1 direction
98
Q

Tell me stage 7 of the derivation of the equation for the pressure of a gas?
(7 steps… 2-way)

A
  • Must find pressure of all particles in all directions
  • For total pressure:
  • use n° of particles x mean pressure per PTCL
  • Energy distribution between particles = random
  • All molecules of gas = different speeds in x direction
  • Find mean pressure per PTCL using rms speed
  • Then multiplying by N (total n° of molecules)
99
Q

What’s the equation for stage 7?
(Derivation of the equation for the pressure of a gas)
(4 things.. gamble, just 1 equation)

A
  • p = mcx2/V
  • p = c̅x2/V
  • p = Nmc̅x2/V
  • Equation 5
100
Q

Tell me stage 8 of the derivation of the equation for the pressure of a gas?
(6 steps… 3-way incl. eqns)

A
  • Equation 5 gives pressure in x direction
  • Mean speed in all directions given by:
  • c̅2 = c̅2x + c̅2y + c̅2z
  • But average velocities in all directions are equal:
  • c̅2 = 3c̅2x
  • c̅2x = 1/3 c̅2
101
Q

Tell me stage 9 of the derivation of the equation for the pressure of a gas?
(5 steps… 2-way screw it)
(Final stage)

A
  • Sub in c̅22 = 1/3 c̅2 into equation 5:
  • p = Nmc̅x2/V
  • pV = Nmc̅x2
  • pV = Nm c̅2/3
  • pV = 1/3Nmc̅2
102
Q

What’s the equation of the internal energy of an ideal gas?
(in data booklet)

A

U = 3/2 nRT

103
Q

Define U
(internal energy of an ideal gas)

A

Internal energy
(J?)

104
Q

Define n
(internal energy of an ideal gas)

A

Moles
(mol)

105
Q

Define R
(internal energy of an ideal gas)

A

Molar gas constant
(m2 kg s-2 K-1 mol-1)
(Psh)

106
Q

Define T
(internal energy of an ideal gas)

A

Temperature
(K)

107
Q

How many stages are there to the derivation of the equation for internal energy of an ideal gas?

A

4 damn long stages

108
Q

For an ideal gas, tell me about its internal energy?
(3 step build up)

A
  • Internal energy = all KE energy
  • It’s the sum of KE of all the particles
  • Internal energy U = N x mean KE of a particle
109
Q

Tell me stage 1 of the derivation of the equation for internal energy of an ideal gas?
(What are the 3 equations… equate them all)

A
  • Start with these equations:
  • pV = nRT
  • pV = 1/3 Nmc̅2
  • KE = 1/2 mv2
  • Equate first 2
  • 1/3 Nmc̅2 =nRT
110
Q

Tell me stage 2 of the derivation of the equation for internal energy of an ideal gas?
(4 steps… 2-way)

A
  • Multiply 2/3 to get the 1/2 needed for KE:
  • 1/2 Nmc̅2 = 3/2nRT
  • 1/2 mc̅2 = 3/2 nRT/N
  • Equation 1
111
Q

Tell me stage 3 of the derivation of the equation for internal energy of an ideal gas?
(7 steps… 3 new steps)

A
  • Equation 1 gives mean KE of a molecule
  • Simplify:
  • Sub n = N/NA into equation 1:
  • 1/2 mc̅2 = 3/2 N/NA/N RT
  • 1/2 mc̅2 = 3/2 R/NA T
  • Sub k = R/NA
  • 1/2 mc̅2 = 3/2 kT

- n/N = 1/Na & R/Na = k
- K.E for 1 particle = 3/2 x 1/Na RT
- Hence: = 3/2 kT

112
Q

Tell me stage 4 of the derivation of the equation for internal energy of an ideal gas?
(7 steps… 5-way ending)

A
  • Internal U = N x mean KE of particle:
  • U = 3/2 NkT
  • Expressed in terms of n° of moles
  • Sub k = R/NA & use n = N/NA
  • Sub k = R/NA
  • Use n = N/NA:
  • U = 3/2 N R/NA T
  • U = 3/2 nRT
113
Q

How to find KE of a mole of monatomic gas?
(2 steps)

A
  • A mole has n = 1
  • U = 3/2 RT
114
Q

How to find mean KE for a molecule?
(5 steps)

A
  • Divide energy for a mole by NA
  • KEone molecule = 3/2 R/NA T
  • Simplify using R = kNA:
  • KEone molecule = (3/2 kNA/NA) T
  • KEone molecule = 3/2 kT
115
Q

These derivations are gruesome

A

A way easier method, just keep writing it….
…. we had to optimise it and now we’re gambling!

116
Q

Past paper questions

A

Plenty

117
Q

First half is lil cheery,

Gamble to make it…

A

But then the second half is a total disaster wat the fa

… Easier…?

The final mock (Physics) (7 decks)

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