Section 8 - Thermal Physics Flashcards
1
Q
What are the main two ways in which energy can transfer from one place to another?
A
- When work is done on an object
2. If one object is hotter than another and conduction, convection or radiation occur
2
Q
What are the two types of energy that molecules in a hot substance will have?
A
Kinetic and potential
3
Q
What is internal energy?
A
The sum of the randomly distributed kinetic and potential energies of the particles in a body
4
Q
What is the symbol for internal energy?
A
U
5
Q
What is internal energy measured in?
A
J
6
Q
What is the first law of thermodynamics?
A
The change of internal energy of the object is equal to the total energy transfer due to work done and heating
7
Q
What is the first law of thermodynamics linked to?
A
Conservation of energy
8
Q
What is a useful outcome of the first law of thermodynamics?
A
If work is being done on an object and it is not increasing its internal energy, then it must have an output rate identical to the work being done on it
9
Q
What happens when a sample is heated?
A
- heat energy supplied increases internal energy
- Ek increases, so mean molecular speed increases
- also mean separation slightly increased so small increase in molecular Ep
10
Q
What happens when a samples changes state?
A
- temperature remains constant
* so mean Ek is constant
11
Q
When a sample is changing state, what is the energy being used for?
A
To break bonds as the sample melts or boils
12
Q
What does heat flow result from?
A
Temperature difference
13
Q
What happens if two objects at different temperatures are placed in thermal contact?
A
Heat flows from the higher to the lower temperature until the temperatures equalise
14
Q
When will two bodies be in thermal equilibrium?
A
When two objects at different temperatures are placed in thermal contact and heat flows from the higher to the lower temperature until the temperatures equalise
15
Q
What happens to internal energy when a substance is hotter?
A
It is increased
16
Q
What does a temperature scale require?
A
Two fixed points with fixed degrees between them
17
Q
What is 0°C in the Celsius scale?
A
Ice point
18
Q
What is 100°C in the Celsius scale?
A
Steam point
19
Q
What is steam point?
A
The temperature of pure steam at standard atmospheric pressure
20
Q
What is the lowest possible temperature on the absolute scale?
A
0K
21
Q
What is definition of the triple point of water?
A
The temperature at which water can exist in all three states
22
Q
What is the value of the triple point of water?
A
273.16 K
23
Q
What is the value of the ice point of water in K?
A
273.15 K
24
Q
How do you convert from Kelvin to Celsius?
A
Add 273.15
25
What happens when you cool a gas within a fixed volume?
Its pressure drops
26
If you plot a graph of pressure against temperature, with different gases, where will the lines intercept?
At absolute 0, on the negative x-axis
27
What unit does the absolute scale use?
Kelvin
28
What does the rise in temperature for a substance being heated depend on?
* mass of substance
* how much energy is put in
* what the substance is
29
What is the equation for the energy required to heat a substance?
E = mcΔθ
30
What is m in E = mcΔθ?
Mass (kg)
31
What is c in E = mcΔθ?
Specific heat capacity (Jkg⁻¹K⁻¹)
32
What is Δθ in E = mcΔθ?
Temperature change (°C or K)
33
What is the specific heat capacity of a substance?
The energy needed to raise the temperature of unit mass of the substance by 1K without change of state
34
What is the symbol for specific heat capacity?
c
35
How can adding an exact amount of energy to a system be achieved?
By doing work on the system
36
In the inversion tube experiment, what happens in terms of energy transfers?
As the contents fall down tube, potential energy is converted into thermal energy
37
If the inversion tube experiment is repeated n times, what is the equation for total energy change?
E = mgLn
38
What is measured in the inversion tube experiment?
In the inversion tube experiment the temperature change of the balls inside the tube
39
What equation can help to calculate specific heat capacity in the inversion tube experiment?
c = gLn / ΔT
40
What experiment can be carried out to find the specific heat capacity of a metal?
* block of metal of known mass in insulated container
* heater and thermometer inserted
* temperature rise measured
* energy supplied = heat current x pd x time
* c = IVt / mΔT
41
To find the specific heat capacity of a liquid instead of a metal, what changes must be made?
Liquid placed inside container instead and stirred
42
What equipment is used to find the specific heat capacity of a liquid?
Calorimeter
43
What must be included in the calculations to find the specific heat capacity of a liquid? Why is this?
The specific heat capacity of the calorimeter, as it absorbs energy
44
What does the rate of change of temperature in boilers and showers create?
A rate of energy input, which is power
45
What is the equation that is useful in continuous flow heating?
IV = P = mcΔT / t
46
What are the units of c?
J kg⁻¹ K⁻¹
47
What does the rate of energy flow to sustain the heating in a system calculate?
The power in Watts
48
Properties of solids?
* maintain shape
* constant volume
* cannot be easily compressed
* molecules/atoms close together and vibrate in fixed positions
49
Properties of liquids?
* flow and take shape of vessel
* constant volume
* cannot be easily compressed
* molecules/atoms are close together and can move around each other
50
Properties of gases?
* flow and take any shape, fill any space
* take the volume of any vessel or space
* can be easily compressed
* molecules/atoms are far apart and are free to move
51
What will be proportional to the energy supplied when a pure substance is heated?
Its temperature
52
Does a material change state at a constant temperature?
Yes
53
Why is the energy transferred to a substance to melt/boil it not obvious or 'hidden'?
Temperature does not change during the change of state
54
What is the energy needed to make a change of state occur?
Latent heat
55
What is latent heat?
The energy needed to make a change of state occur
56
What is the latent heat of fusion?
The energy needed to melt a substance
57
What is the latent heat of vaporisation?
The energy needed to evaporate a substance
58
What is specific latent heat?
How much energy is needed to make a unit mass of a pure substance change state
59
What are the units for specific latent heat?
J kg⁻¹
60
On a temperature-time graph, what does the gradient represent?
The rate of change of temperature
61
On a temperature-time graph, what will a steeper gradient show?
That state heats more quickly - and has a lower specific heat capacity
62
On a temperature-time graph, what is the length of time to change state proportional to?
The specific latent heat for each state change
63
What is the equation for specific latent heat?
E = ml
64
What does E stand for in E = ml?
Energy (J)
65
What does m stand for in E = ml?
Mass (kg)
66
What does l stand for in E = ml?
Specific latent heat (Jkg⁻¹)
67
What is the specific latent heat of fusion of ice?
3.3. x 10³ Jkg⁻¹
68
What is the specific latent heat of vaporisation of water?
22.6 x 10³ Jkg⁻¹
69
What is the pressure of a gas?
The force per unit area that is exerts at right angles to surface
70
What is pressure affected by?
* temperature
* volume
* mass of gas particles
71
What are the units of pressure?
pascals (Pa or Nm⁻²)
72
What type of collisions do gas molecules have with the walls of the container?
Elastic
73
Why do gas molecules move at the same speed after they have collided with the container wall?
The collisions are elastic
74
What is the magnitude of pressure proportional to?
The rate of collisions with the container wall
75
How can the pressure of a gas be increased?
* increasing temperature - particles move faster
* reducing volume of container - increases chance of particles colliding with wall
* adding more gas - increasing the number of particles
76
What is Boyle's law in words?
The pressure of a fixed mass of gas at constant temperature is inversely proportional to its volume
boils have volume and are hot (volume + temp)
77
What is Boyle's law in equations?
p ∝ 1/V
pV = constant
78
What is an isothermal change?
An experiment done at constant temperature
79
What is an experiment done at constant temperature?
Isothermal change
80
For a Boyle's law experiment at constant temperature, what shape will a pressure-volume graph be?
Downwards curve
81
How could a pressure-volume graph for a Boyle's law experiment be made into a straight line?
Plot p against 1/V
82
What is Charles' law?
Reducing the temperature of a gas but maintaining the same pressure causes the volume to decrease
83
In Charles' law, what does volume increase in proportion to?
Absolute temperature
84
In a graph showing Charles' law, where will the x-intercept always occur?
At -273.15 °C (absolute zero)
85
What is the equation for Charles' law?
V = constant T
86
What is an experiment done at constant pressure?
An isobaric change
87
What is an isobaric change?
An experiment done at constant pressure
88
In a Charles' law experiment, what condition must there be for the x-intercept to be at absolute zero?
The gas must be ideal
89
What must happen if a volume of gas is compressed but the pressure is maintained?
Heat must be transferred
90
What happens when you reduce the temperature of a gas at a fixed volume?
Pressure is reduced
91
What equation relates to the pressure law?
p = constant times T
92
What has the same shape as a Charles' law (volume-temperature) graph?
Pressure against temperature
93
What are the three relationships between volume, pressure and temperature?
* Boyle's law
* Charles' law
* The pressure law
94
What is an ideal gas?
One which obeys the gas law exactly
95
When can real gas behaviour be classed as ideal?
When gases are considered at low pressures and higher temperatures
96
What can the gas laws be combined to give?
PV/T = constant
or
P₁V₁ / T₁ = P₂V₂ / T₂
97
What must be true of a gas to be ideal?
* particles themselves can be thought of as taking up no volume
* no significant forces between particles
* motion of particles is random
98
What is Brownian motion?
The random movement of particles in a fluid
99
What is responsible for diffusion?
Brownian motion
100
Why must the same volume of two gases at the same temperature contain the same number of particles?
Because the particles in an ideal gas take up no volume themselves
101
What is the word definition of the Avogadro constant?
The number of carbon atoms in 12g of carbon-12
102
Why did the definition of Avogadro's constant change from using hydrogen to carbon?
It is difficult to get a pure enough sample of Hydrogen-1 without isotopes being present
103
What is the value of the Avogadro constant?
6.023 x 10²³
104
How many
| particles does one mole of a pure substance contain?
Avogadro's number
105
What is the molarity of a sample?
How many moles in contains - unit is mol
106
What is the molar mass of a sample?
The mass of 1 mol in kgmol⁻¹
107
Equation for number of molecules in a specific mass?
Ms = NA x Ms / Molar mass
108
How is the constant calculated in pV/T = constant?
* plot pV against T (in K)
* straight line through origin - find gradient (nR)
* rearrange formula: pV = nRT
109
What is the Boltzmann constant?
A way of using the ideal gas equation to know the number of particles
110
What equation is formed when the Boltzmann constant is used in pV/T = constant?
pV = NkT
111
What does k equal in pV = NkT?
k= Boltzmann constant = R/NA = 1.38 x 10⁻²³ JK⁻¹
112
How to calculate the root mean square?
Square every value, divide by the number of data points then square root the total
113
What does the graph of the speeds of molecules in a gas look like?
A bell curve
114
What is a useful value to compare the speeds of molecules at different temperatures?
Root mean square of their speeds
115
What are the 6 assumptions that have to be made to create a kinetic theory equation?
* the particles themselves take up no volume
* there is no force of attraction between the particles
* their motion is random
* their collisions are elastic
* the length of time of the collisions against the walls of the container and each other are negligible
* Newton's laws of motion can be applied
116
What are the three factors that affect the pressure of a gas in a given volume?
* mass of molecules
* speed of molecules
* how many molecules there are in the container
117
What is the theoretical equation for an ideal gas?
PV = 1/3 Nmc²
118
What does P mean in PV = 1/3 Nmc²?
Pressure (Pa)
119
What does V mean in PV = 1/3 Nmc²?
Volume (m³)
120
What does N mean in PV = 1/3 Nmc²?
Number of molecules
121
What does m mean in PV = 1/3 Nmc²?
Mass of one molecule (kg)
122
What does c mean in PV = 1/3 Nmc²?
Average molecular speed (ms⁻¹)
123
What happens when you combine the theoretical equation for ideal gas and the ideal gas equation?
1/2mc² = 3RT/2Na = 3/2 kt
124
How is E = 3/2mc² formed from 1/2mc² = 3RT/2Na = 3/2 kt?
Because 1/2 mc² is the mean kinetic energy of a gas molecule
125
What is the temperature of a gas a mean of?
The average kinetic energy of the particles
126
How can you calculate the mean kinetic energy of the molecules?
By dividing total energy by the number of particles
127
The equation to calculate mean kinetic energy of molecules is found on the dat sheet. what does everything stand for?
E = 1/2 m(c RMS)²= 1.5 kT = 3RT/2Na
E = 1/2 m(c RMS)²= 1.5 kT = 3RT/2Na
```
m= mass (kg)
crms= means uspeed
k= Boltzmann constant
T= temperature (K)
R=molar gas constant
Na= avogadro's number
```
128
What are the two useful formulas to find the mean kinetic energy of molecules?
* E = 1/2 m(c RMS)²
| * E = 3/2kT
129
How can the total energy of n moles of a gas at temperature T kelvin be calculated?
3/2 nRT
130
How can internal energy be calculated?
3/2 nRT
131
Make sure you practice how to derive the kinetic energy equation.
Ok.
132
Do all the particles in a body travel at the same speed?
No
133
What does the distribution of particle speeds in a body depend on?
The temperature.
134
How does temperature affect the average kinetic energy of the particles?
The higher the temperature, the higher the average kinetic energies.
135
What does higher kinetic energy mean for the average particle speed and the speed distribution graph?
Average particle speed increases and the distribution curve becomes more spread out.
136
What does the graph for number of particles vs particle speed look like?
137
Do all the particles in the body have the same potential energies?
No
138
What determines the potential energy of the particles in a body?
Their relative positions.
139
Define internal energy.
The sum of the randomly distributed kinetic and potential energies of all the particles in a body.
140
How is energy transferred between particles in a system?
Collisions between particles.
141
Does a closed system have a constant total internal energy?
| What are the conditions?
Yes, as long as:
• It’s not heated or cooled
• No work is done
142
How can the internal energy of a system be increased?
* Heating it
| * Doing work on it
143
Does internal energy change when there when particles collide in a closed system, providing there is no work being done and temperature is constant?
No it stays constant.
| Average speed of the particles also stays constant
144
Have can you decrease internal energy?
Doing work to to remove energy or cooling the system
145
During a change of state, what happens to kinetic and potential energies?
* Kinetic energy -> Constant
| * Potential energy -> Changes
146
What happens to temperature when a substance changes state?
Stays the same
147
On a digital thermometer, what will happen to the rate of temperature increase when an object changes state?
Rate of temperature increase decreases
148
What does a graph of temperature against internal energy look like during a change of state?
149
Will heat transfer from hot objects to cold objects or the other way around?
Heat is always transferred from hotter substances to cooler substances.
150
In particle terms what happens when heat is transferred from a hot object to a cold object?
The particle with more energy transfers some energy to the particle with less energy.
151
What makes heat transfer faster?
A higher difference in temperature between the two substances
152
What is the equation for internal energy?
Internal energy = Kinetic energy + Potential energy
153
In radiation, do hotter or colder objects radiate heat quicker?
Hotter
154
Does internal energy change when there is a change of state? Why?
Yes, because the potential energy of the particles is increased.
155
Define specific heat capacity.
The amount of energy needed to raise the temperature of 1kg of a substance by 1K (or 1 degree C).
156
What is the symbol for specific heat capacity?
c
157
What are the units for specific heat capacity?
J/kg/K or J/kg/°C
158
What is the equation for energy change relating to specific heat capacity?
Q = mcΔθ
```
Where:
• Q = Energy change (J)
• m = Mass (kg)
• c = Specific heat capacity (J/kg/K or J/kg/°C)
• θ = Temperature (K or °C)
```
159
What is the unit for the mass used in the specific heat capacity equation?
kg
160
How can you investigate the effect on temperature by changing:
Mass?
Type of material (=changes specific heat capacity)?
Rate of energy transfer?
161
What should you include in a risk assessment of investigating factors that effect change in temperature?
Precautions when placing an electrical heater in water and the fact that the water will be hot.
162
When investigating factors that effect change in temperature, why will c be too high?
How can you avoid this?
Some of the energy from the heater is transferred to the air and the container.
You can reduce the error by starting below and finishing above room temperature to cancel out gains and losses.
163
What technique can be used to measure specific heat capacity?
Using a continuous-flow calorimeter.
164
What is continuous-flow heating?
When a fluid flows continuously over a heating element, so energy is transferred to it.
165
Describe the set-up of a continuous-flow calorimeter.
* Heating element is placed in a tube of water, connected to an ammeter and voltmeter
* At one end of the tube is the water-in and at the other end is the water-out
* A thermometer at each end measures the temperature of water going in and going out
166
Describe how a continuous-flow calorimeter can be used to work out the specific heat capacity of a liquid.
1) Set up the equipment as such:
• Heating element is placed in a tube of water, connected to an ammeter and voltmeter
• At one end of the tube is the water-in and at the other end is the water-out
• A thermometer at each end measures the temperature of water going in and going out
2) Let the liquid flow until the temperature of the water going out is constant
3) Record the flow rate, time, temperature difference, current and voltage.
4) Energy supplied is Q = mcΔθ + H, where H is heat lost to the surroundings.
5) Repeat the experiment, changing the potential difference of the jolly and the flow rate so that Δθ is constant. There should now be an equation for each experiment.
6) The values of c, Δθ and H are the same, so Q₂ - Q₁ = (m₂ - m₁)cΔθ
7) So c = (Q₂ - Q₁) / (m₂ - m₁)Δθ where Q is just equal to VIt.
167
Define specific latent heat.
The quantity of thermal energy require to change the state of 1kg of a substance.
168
What is the unit for specific latent heat?
J/kg
169
Give the equation for the energy change relative to specific latent heat.
Q = ml
Where:
• m = Mass (kg)
• l = Specific latent heat (J/kg)
170
What unit for mass is used in specific latent heat calculations?
kg
171
What are the two types of specific latent heat?
* Specific latent heat of fusion -> Solid to liquid
| * Specific latent heat of vaporisation -> Liquid to gas
172
What is the symbols for specific latent heat?
l
173
What is the lowest possible temperature called?
Absolute zero
174
What is absolute zero?
* The lowest possible temperature, where particles have the minimum possible kinetic energy
* 0K
175
How is the temperature is Kelvin related to the particle’s energy?
They are directly proportional.
176
How does the increment on the Kelvin scale differ from the Celsius scale?
They are the same (so 1K = 1°C).
177
Give the equation linking Kelvin and Celsius.
K = C + 273
178
What is the temperature of absolute zero in Kelvin and Celsius?
* 0K
| * -273°C
179
Give 100°C in Kelvin.
373K
180
Give 0°C in Kelvin.
273K
181
Which temperature scale is used in thermal physics?
Kelvin
182
What are the three gas laws and their equations?
* Boyle’s Law -> pV = constant
* Charles’ Law -> V/T = constant
* Pressure Law -> p/T = constant
183
What is an assumption of the 3 gas laws?
The mass of the gas is constant.
184
What is Boyle’s Law?
* pV = Constant
| * At a constant temperature, the pressure and volume of a gas are inversely proportional
185
Describe the graph for Boyle’s Law.
* Pressure against volume plotted
* Like a 1/x curve, depending on the temperature
* The higher the temperature, the further the curve is from the origin.
186
How does temperature affect the graph for Boyle’s Law (p-V)?
The higher the temperature, the further the curve is from the origin.
187
Why does Boyles Law happen (particles)?
If you reduce the volume, the particles will be closer together and collide more often = pressure increases
188
Why aren't perfect gases perfect? (which law don't they follow perfectly and why?)
Perfect gases aren't quite perfect as they don't follows Boyles law perfectly:
Boyles law assumes that the particles don't have any size or (more importantly) volume of their own.
189
What is Charles’ Law?
* V/T = Constant
| * At a constant pressure, the volume of a gas is directly proportional to its absolute temperature
190
Describe the graph for Charles’ Law.
* Volume against temperature plotted
* Straight line with positive gradient
* x-intercept is at -273°C or 0K
191
Why does Charles law happen (particles)?
Heat gas = particles gain KE = move more quickly = (at a constant pressure) they move further apart = volume of gas increases
192
What is the Pressure Law?
* p/T = Constant
| * At a constant volume, the pressure of a gas is directly proportional to the temperature
193
Describe the graph for the Pressure Law.
* Pressure against temperature is plotted
* Straight line with positive gradient
* x-intercept is at -273°C or 0K
194
What happens in the pressure law (particles)?
Heat gas = particles gain KE = Moves faster = (If volume is constant) particles collide with each other more often and at higher speeds = increasing pressure
195
What is an ideal gas?
One that obeys all 3 gas laws.
196
Describe an experiment to investigate Boyle’s Law.
1) Set up a marked sealed tube with air at the top and oil at the bottom.
2) Connect the tube to a Bourdon gauge (pressure gauge) and a pump to pump more oil in.
3) Increase the pressure from atmospheric pressure using the pump. Make sure to keep the temperature constant.
4) At each pressure, record the pressure (off the Bourdon gauge) and the volume of air (off the sealed tube) by using the radius and length to find v).
5) Repeat 2 more times and average.
6) Plot a graph of p against 1/V. This should give a straight line.
197
Describe an experiment to investigate Charles’ Law.
1) Set up a capillary tube that’s sealed at the bottom and that has a drop of sulphuric acid trapped halfway up the tube. This traps a column of air between the drop and bottom of the tube.
2) Place the tube next to a ruler in a beaker of near-boiling water. Also place a thermometer in the beaker.
3) As the water cools, record the height of the air and temperature at several temperatures.
4) Repeat 2 more times and average.
5) Plot a graph of height against temperature. This should give a straight line. Since height is proportional to volume, this proves Charles’ Law.
198
Remember to practise drawing out the setup for the gas law experiments.
Pg 111 of revision guide
199
What is relative molecular mass?
The sum of the mass of all the atoms that make up a molecule, relative to 1/12th the mass of a carbon-12 atom.
200
What is the relative mass of carbon-12?
12
201
What is the relative molecular mass of carbon dioxide? (1 carbon-12 molecule and 2 oxygen-16 molecules)
12 + 16 + 16 = 44
202
What is the molar mass of a gas?
The mass of one mole of that gas, usually in grams
203
What is Avogadro’s constant?
* 6.02 x 10^23 mol^-1
* It is the number of molecules in a mole
(It is the number of atoms in 12g of Carbon 12 - 6)
204
What is the symbol for Avogadro’s constant?
NA (where A is in subscript)
205
What can be said about the molar mass and the relative molecular mass?
They are the same value.
206
If the the molar mass and the relative molecular mass are the same then why is the molar mass of oxygen 32g and relative molecular mass 16.0?
Because there are two molecules in oxygen (it's diatomic) so the molecular mass doubles to get the molar mass.
207
What is the symbol for the number of moles?
n
208
What is the equation for the number of molecules in a gas?
N = n x NA
Where:
• N = Number of molecules
• n = Moles
• NA = Avogadro’s constant
209
What is the ideal gas equation?
pV = nRT
```
Where:
• p = Pressure (Pa)
• V = Volume (m³)
• n = No. of moles
• R = Molar gas constant = 8.31J/mol/K
• T = Temperature (K)
```
210
How is the ideal gas equation formed?
By combining the 3 gas laws.
211
What units for pressure, volume and temperature are used in the ideal gas equation?
* Pressure -> Pa
* Volume -> m³
* Temperature -> K
212
When does the ideal gas equation work best?
At low pressures and fairly high temperatures.
213
What is Boltzmann’s constant?
* Equal to R/NA
| * It is the gas constant for one particle of gas (as opposed to R, which is the gas constant for one mole of gas)
214
What is the symbol for Boltzmann’s constant?
k
215
What is the difference between R and k?
* R = The gas constant for one mole of a gas
| * k = The gas constant for one particle of a gas
216
What is the value of Boltzmann’s constant?
1.38 x 10⁻²³ J/K
217
What do the symbols stand for?
pV = NkT
pV = NkT
```
Where:
• p = Pressure (Pa)
• V = Volume (m³)
• N = No. of molecules of gas
• k = Boltzmann’s constant = 1.38 x 10⁻²³ J/K
• T = Temperature (K)
```
218
What are the two equations for gases?
* Ideal gas equation -> pV = nRT
| * Equation of state -> pV = NkT
219
What must happen in order for a gas to expand or contract at constant pressure?
Work must be done, either by the gas or on the gas.
220
What type of energy transfer most commonly occurs when a gas expands or contracts?
Heat transfer - e.g. heating a gas filled balloon makes it expand
221
What is the equation for the work done to expand a gas?
W = p x ΔV
Where:
• W = Work done (J)
• p = Pressure (Pa)
• ΔV = Change in volume (m³)
(NOTE: This only applies when pressure is constant.)
222
How can the work done to expand a gas be found using a p-V graph?
It is the area under the graph.
223
Write out how to derive the equations for the pressure of an ideal gas.
Pg 114 of revision guide
224
IMPORTANT: Remember to practise deriving the equations for the pressure of an ideal gas.
Pg 114 of revision guide
225
How do you derive the equation of the pressure of a single particle in an ideal gas?
226
How do you derive the equation of the pressure of an ideal gas, from the equation of pressure of a particle in the gas?
What other equations can you get from this?
227
For a single air particle colliding with the wall of its container, what is the force exerted? Derive this.
In a cubic box with sides of length l, containing N particles, each of mass m:
• Strikes the wall A with momentum mu and returns with momentum -mu
• Change in momentum = -2mu
• Collisions per second = u/2l (since the particles only strikes wall A every full lap)
• F = -2mu x u/2l = -mu²/l
228
Derive the equation for the pressure on one wall of a box due to a gas.
In a cubic box with sides of length l, containing N particles, each of mass m:
• Strikes the wall A with momentum mu and returns with momentum -mu
• Change in momentum = -2mu
• Collisions per second = u/2l (since the particles only strikes wall A every full lap)
• F = -2mu x u/2l = -mu²/l
For particles of various velocity:
• F = m(u₁² + u₂² + ...) / I
• û² = (u₁² + u₂² + ...) / N
• F = Nmû² / I
• Pressure = Force / Area = (Nmû² / I) / l² = Nmû² / l³ = Nmû² / V
(NOTE: Not given in exam!)
229
Derive the equation for the pressure on all the walls of a box due to a gas.
* First, derive the equation for just one wall: F = Nmû² / V
* When a gas particle moves in 3D, the speed (c) is calculated using Pythagoras’ theorem
* c² = u² + v² + w² (where u, v and w are components of the velocity)
* c²(bar) = u²(bar) + v²(bar) + w²(bar)
* Since the particles move randomly, u²(bar) = v²(bar) = w²(bar), so:
* u²(bar) = c²(bar) / 3
* Substituting back into original equation:
* pV = 1/3 Nmc²(bar)
230
What is the equation for the pressure of a gas in a box in 3 directions?
pV = 1/3 Nmc²(bar)
```
Where:
• p = Pressure (Pa)
• V = Volume (m³)
• N = Number of molecules
• m = Mass of particle (kg)
• c²(bar) = Mean square speed (m²/s²)
```
231
What does c²(bar) symbolise?
* Mean square speed
| * It is the average of the square speeds of all of the particles
232
What is the root mean square speed?
* The root of c²(bar)
| * It is a measure of the typical speed of a particle
233
What is the symbol for the root mean square speed?
c(rms)
| Where rms is subscript
234
Give the equation that links the rms speed and the mean square speed.
r.m.s. speed = √(mean square speed)
√ c²(bar) = c(rms)
235
What are the units for the root mean square speed?
m/s
236
What are the two important speeds in ideal gas equations?
* Mean square speed
| * r.m.s speed
237
What are some of the simplifying assumptions used in kinetic theory?
1) Molecules continually move about randomly.
2) Motion of molecules follows Newton’s laws.
3) Collisions between molecules or at the walls of the container are perfectly elastic.
4) Except for during collisions, the molecules always move in a straight line.
5) Any forces that act during collisions last for much less time than the time between collisions.
6) All molecules of the gas are identical.
7) The gas contains a large number of molecules.
8) Molecules have negligible volume compared with the volume of the container (i.e. they act as point masses)
238
What are the simplified kinetic theory assumptions and how do you remember it?
239
What are some of the defining features of an ideal gas?
* Obeys the 5 simplifying assumptions of kinetic theory
* Follow the 3 gas laws
* Internal energy dependent only on the kinetic energy of the particles
240
Why is the potential energy of an ideal gas 0?
There are no forces between particles except when they are colliding.
241
When do real gases behave like ideal gases?
When the pressure is low and the temperature is high.
242
If temperature is increased and volume is fixed, why does pressure increase (collisions and force)?
More collisions between molecule and the walls in a given amount of time.
On average, a collision will result in a larger change in momentum (higher average speed), and so exert a larger force on the walls on the container.
243
If temperature is increased and pressure is fixed, why does volume increase? Why does pressure stay constant?
If volume is larger, there will be a longer time between molecule-wall collisions, so rate of change of momentum and therefore the force on the walls of the container will be reduced.
As volume increases, the surface area of the walls increases. Pressure is defined as force per unit area, increasing area stops the pressure from increasing.
244
What are the 3 equations for the average kinetic energy of a particle in a gas?
* KE = 1/2 m(c(rms))²
* KE = 3/2 kT
* KE = 3/2 RT/N(A)
```
Where:
• KE = Kinetic energy (J)
• m = Mass of particle (kg)
• c(rms) = Root mean square speed (m/s)
• k = Boltzmann’s constant = 1.38 x 10⁻²³
• T = Temperature (K)
• R = Molar gas constant = 8.31
• N(A) = Avogadro constant = 6.02 x 10⁻²³
```
245
Derive the 3 equations for the average kinetic energy of a particle in a gas.
* pV = nRT
* pV = 1/3 Nm(c(rms))²
* Therefore: 1/3 Nm(c(rms))² = nRT
* 1/2 Nm(c(rms))² = 3/2 nRT/N
* 1/2 Nm(c(rms))² is the average kinetic energy of a particle.
* Substitute Nk for nR:
* 1/2 m(c(rms))² = 3/2 kT
* Since the Boltzmann constant is equal to R/N(A):
* 1/2 m(c(rms))² = 3/2 RT/N(A)
246
How is the average kinetic energy of a gas related to the absolute temperature?
It is proportional.
247
Which equation demonstrates the relationship between average kinetic energy of a gas and the absolute temperature?
* 1/2 m(c(rms))² = 3/2 kT
| * This shows that the kinetic energy is directly proportional to T.
248
With the number of molecules and the average kinetic energy of the molecules, how do you find the total kinetic energy of the molecules in a gas?
Average kinetic energy (of a molecule) x total number of of molecules
249
What are empirical laws?
Laws based on observation and evidence, without any explanation why.
250
What are theoretical laws?
Laws that are based on assumptions and derivations from knowledge and theories we already had, giving an explanation for certain phenomena.
251
What is the difference between empirical and theoretical laws?
* Empirical laws - Predict what will happen, but don’t explain why.
* Theoretical laws - Predict what will happen based on existing knowledge and theories.
252
With gases, what laws are empirical and what laws are theoretical?
* Empirical - Gas laws, ideal gas laws -> remember empirical LAWS: gas + ideal gas LAWS
* Theoretical - Kinetic theory -> remember THEORIES: kinetic THEORY
253
For an ideal gas, internal energy = ?
Kinetic energy of atoms
254
Describe how our understanding of gases has changed over time.
* Ancient Greek and Roman philosophers including Democritus had ideas about gases 2000 years ago, some of which were close to what we now know is true
* Robert Boyle discovered relationship between pressure and volume at a constant temperature in 1662
* Jacques Charles discovered the volume of gas is proportional to temperature at a constant pressure in 1787
* Guillaume Amontons discovered that at a constant volume, temperature is proportional to pressure, in 1699. It was rediscovered by Joseph Louis Gay-Lussac in 1809.
* In the 18th Century, Daniel Bernoulli explained Boyle’s Law by assuming that gases were made up of tiny particles - This was the start of kinetic theory, but it took over 200 years before this was widely accepted.
* In 1827, Robert Brown discovered Brownian motion, which helped support kinetic theory.
255
Describe who discovered each gas law and when this happened.
* Boyle’s Law -> Robert Boyle in 1662
* Charles’ Law -> Jacques Charles in 1787
* Pressure Law -> Guillaume Amontons in 1699 and then Joseph Louis Gay-Lussac in 1809
256
Who, when and how discovered the beginnings of kinetic theory?
* Daniel Bernoulli
* In 18th Century
* Explained Boyle’s Law by assuming that gases were made up of tiny particles
257
Did Daniel Bernoulli’s become accepted immediately?
No, it it wasn’t until the 1900s when Einstein was able to use kinetic theory to make predictions for Brownian motion that atomic and kinetic theory became widely accepted.
258
Why can’t scientific ideas be accepted immediately?
The ideas have to be independently validated or anyone could just make up any nonsense.
259
What is the main support for kinetic theory?
| Who used kinetic theory to prove this?
Einstein used kinetic theory to make predictions for Brownian motion.
260
What is kinetic theory?
The body of theory that explains the physical properties of matter in terms of the motion of its particles.
261
Who and when discovered Brownian motion?
Robert Brown in 1827
262
What is Brownian motion and what does it provide evidence for?
• It is the zigzag, random motion of particles in a fluid.
• This supports the existence of atoms and kinetic particle theory.
(Helped support evidence that everything is made from atoms)
263
What explains the random movement of particles in Brownian motion?
What did small objects did Einstein use to explain this?
Einstein explained how the the random motion of the pollen grains were a result of....
…the collisions with fast, randomly-moving particles in the fluid.
264
How can Brownian motion be seen?
When large, heavy particles (e.g. smoke) are moved with Brownian motion by smaller, lighter particles (e.g. air) travelling at high speeds.
265
Why does Boyles Law happen (particles)?
If you reduce the volume, the particles will be closer together and collide more often = pressure increases.
