Section 8 - Thermal Energy Transfer Flashcards
1
Q
Do all the particles in a body travel at the same speed?
A
No
2
Q
What does the distribution of particle speeds in a body depend on?
A
The temperature.
3
Q
How does temperature affect the average kinetic energy of the particles?
A
The higher the temperature, the higher the average kinetic energies.
4
Q
Remember to practice drawing out the graphs for number of particles vs particle speed.
A
Pg 108 of revision guide
5
Q
Do all the particles in the body have the same potential energies?
A
No
6
Q
What determines the potential energy of the particles in a body?
A
Their relative positions.
7
Q
Define internal energy.
A
The sum of the randomly distributed kinetic and potential energies of all the particles in a body.
8
Q
How is energy transferred between particles in a system?
A
Collisions between particles.
9
Q
Does a closed system have a constant total internal energy?
A
Yes, as long as:
• It’s not heated or cooled
• No work is done
10
Q
How can the internal energy of a system be increased?
A
- Heating it
* Doing work on it
11
Q
During a change of state, what happens to kinetic and potential energies?
A
- Kinetic energy -> Constant
* Potential energy -> Changes
12
Q
What is the equation for internal energy?
A
Internal energy = Kinetic energy + Potential energy
13
Q
Does internal energy change when there is a change of state? Why?
A
Yes, because the potential energy of the particles is increased.
14
Q
Define specific heat capacity.
A
The amount of energy needed to raise the temperature of 1kg of a substance by 1K.
15
Q
What is the symbol for specific heat capacity?
A
c
16
Q
What are the units for specific heat capacity?
A
J/kg/K or J/kg/°C
17
Q
What is the equation for energy change relating to specific heat capacity?
A
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)
18
Q
What is the unit for the mass used in the specific heat capacity equation?
A
kg
19
Q
What technique can be used to measure specific heat capacity?
A
Using a continuous-flow calorimeter.
20
Q
What is continuous-flow heating?
A
When a fluid flows continuously over a heating element, so energy is transferred to it.
21
Q
Describe the set-up of a continuous-flow calorimeter.
A
- 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
22
Q
Describe how a continuous-flow calorimeter can be used to work out the specific heat capacity of a liquid.
A
1) Set up the equipment as on pg 109 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)cΔθ where Q is just equal to VIt.
23
Q
Define specific latent heat.
A
The quantity of thermal energy require to change the state of 1kg of a substance.
24
Q
What is the unit for specific latent heat?
A
J/kg
25
Give the equation for the energy change relative to specific latent heat.
Q = ml
Where:
• m = Mass (kg)
• l = Specific latent heat (J/kg)
26
What unit for mass is used in specific latent heat calculations?
kg
27
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
28
What is the symbols for specific latent heat?
l
29
What is the lowest possible temperature called?
Absolute zero
30
What is absolute zero?
* The lowest possible temperature, where particles have the minimum possible kinetic energy
* 0K
31
How is the temperature is Kelvin related to the particle’s energy?
They are directly proportional.
32
How does the increment on the Kelvin scale differ from the Celsius scale?
They are the same (so 1K = 1°C).
33
Give the equation linking Kelvin and Celsius.
K = C + 273
34
What is the temperature of absolute zero in Kelvin and Celsius?
* 0K
| * -273°C
35
Give 100°C in Kelvin.
373K
36
Give 0°C in Kelvin.
273K
37
Which temperature scale is used in thermal physics?
Kelvin
38
What are the three gas laws and their equations?
* Boyle’s Law -> pV = constant
* Charles’ Law -> V/T = constant
* Pressure Law -> p/T = constant
39
What is an assumption of the 3 gas laws?
The mass of the gas is constant.
40
What is Boyle’s Law?
* pV = Constant
| * At a constant temperature, the pressure and volume of a gas are inversely proportional
41
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.
(See diagram pg 110 of revision guide)
42
How does temperature affect the graph for Boyle’s Law (p-V)?
The higher the temperature, the further the curve is from the origin.
43
What is Charles’ Law?
* V/T = Constant
| * At a constant pressure, the volume of a gas is directly proportional to its absolute temperature
44
Describe the graph for Charles’ Law.
* Volume against temperature plotted
* Straight line with positive gradient
* x-intercept is at -273°C or 0K
(See diagram pg 110 of revision guide)
45
What is the Pressure Law?
* p/T = Constant
| * At a constant volume, the pressure of a gas is directly proportional to the temperature
46
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
(See diagram pg 110 of revision guide)
47
What is an ideal gas?
One that obeys all 3 gas laws.
48
Remember to practice drawing out the diagrams for the 3 gas laws.
Pg 110 of revision guide
49
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 (off the sealed tube).
5) Repeat 2 more times and average.
6) Plot a graph of p against 1/V. This should give a straight line.
50
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.
51
Remember to practise drawing out the setup for the gas law experiments.
Pg 111 of revision guide
52
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.
53
What is the relative mass of carbon-12?
12
54
What is the relative molecular mass of carbon dioxide?
12 + 16 + 16 = 44
55
What is the molar mass of a gas?
The mass of one mole of that gas.
56
What is Avogadro’s constant?
* 6.02 x 10^23
| * It is the number of molecules in a mole
57
What is the symbol for Avogadro’s constant?
NA (where A is in subscript)
58
What can be said about the molecular mass and molar mass of a substance?
They are the same value.
59
What is the symbol for the number of moles?
n
60
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
61
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)
```
62
How is the ideal gas equation formed?
By combining the 3 gas laws.
63
What units for pressure, volume and temperature are used in the ideal gas equation?
* Pressure -> Pa
* Volume -> m³
* Temperature -> K
64
When does the ideal gas equation work best?
At low pressures and fairly high temperatures.
65
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)
66
What is the symbol for Boltzmann’s constant?
k
67
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
68
What is the value of Boltzmann’s constant?
1.38 x 10⁻²³ J/K
69
What is the equation of state?
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)
```
70
What are the two equations for gases?
* Ideal gas equation -> pV = nRT
| * Equation of state -> pV = NkT
71
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.
72
What type of energy transfer most commonly occurs when a gas expands or contracts?
Heat transfer
73
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.)
74
How can the work done to expand a gas be found using a p-V graph?
It is the area under the graph.
75
IMPORTANT: Remember to practise deriving the equations for the pressure of an ideal gas.
Pg 114 of revision guide
76
Write out how to derive the equations for the pressure of an ideal gas.
Pg 114 of revision guide
77
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
78
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!)
79
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)
80
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)
```
81
What does c²(bar) symbolise?
* Mean square speed
| * It is the average of the square speeds of all of the particles
82
What is the root mean square speed?
* The root of c²(bar)
| * It is a measure of the typical speed of a particle
83
What is the symbol for the root mean square speed?
c(rms)
| Where rms is subscript
84
Give the equation that links the rms speed and the mean square speed.
r.m.s. speed = √(mean square speed)
√ c²(bar) = c(rms)
85
What are the units for the root mean square speed?
m/s
86
What are the two important speeds in ideal gas equations?
* Mean square speed
| * r.m.s speed
87
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.
88
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
89
Why is the potential energy of an ideal gas 0?
There are no forces between particles except when they are colliding.
90
When do real gases behave like ideal gases?
When the pressure is low and the temperature is high.
91
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
```
92
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)
93
How is the average kinetic energy of a gas related to the absolute temperature?
It is proportional.
94
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.
95
What are empirical laws?
Laws based on observation and evidence, without any explanation why.
96
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.
97
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.
98
With gases, what laws are empirical and what laws are theoretical?
* Empirical - Gas laws
| * Theoretical - Kinetic theory
99
For an ideal gas, internal energy = ?
Kinetic energy of atoms
100
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.
101
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
102
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
103
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.
104
Why can’t scientific ideas be accepted immediately?
The ideas have to be independently validated or anyone could just make up any nonsense.
105
What is the main support for kinetic theory?
Brownian motion
106
What is kinetic theory?
The body of theory that explains the physical properties of matter in terms of the motion of its particles.
107
Who and when discovered Brownian motion?
Robert Brown in 1827
108
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.
109
What explains the random movement of particles in Brownian motion?
Collisions with fast, randomly-moving particles in the fluid.
110
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.
