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
What does higher kinetic energy mean for the average particle speed and the speed distribution graph?
A
Average particle speed increases and the distribution curve becomes more spread out.
5
Q
What does the graph for number of particles vs particle speed look like?
A
6
Q
Do all the particles in the body have the same potential energies?
A
No
7
Q
What determines the potential energy of the particles in a body?
A
Their relative positions.
8
Q
Define internal energy.
A
The sum of the randomly distributed kinetic and potential energies of all the particles in a body.
9
Q
How is energy transferred between particles in a system?
A
Collisions between particles.
10
Q
Does a closed system have a constant total internal energy?
What are the conditions?
A
Yes, as long as:
• It’s not heated or cooled
• No work is done
11
Q
How can the internal energy of a system be increased?
A
- Heating it
* Doing work on it
12
Q
Does internal energy change when there when particles collide in a closed system, providing there is no work being done and temperature is constant?
A
No it stays constant.
Average speed of the particles also stays constant
13
Q
Have can you decrease internal energy?
A
Doing work to to remove energy or cooling the system
14
Q
During a change of state, what happens to kinetic and potential energies?
A
- Kinetic energy -> Constant
* Potential energy -> Changes
15
Q
What happens to temperature when a substance changes state?
A
Stays the same
16
Q
On a digital thermometer, what will happen to the rate of temperature increase when an object changes state?
A
Rate of temperature increase decreases
17
Q
What does a graph of temperature against internal energy look like during a change of state?
A
18
Q
Will heat transfer from hot objects to cold objects or the other way around?
A
Heat is always transferred from hotter substances to cooler substances.
19
Q
In particle terms what happens when heat is transferred from a hot object to a cold object?
A
The particle with more energy transfers some energy to the particle with less energy.
20
Q
What makes heat transfer faster?
A
A higher difference in temperature between the two substances
21
Q
What is the equation for internal energy?
A
Internal energy = Kinetic energy + Potential energy
22
Q
In radiation, do hotter or colder objects radiate heat quicker?
A
Hotter
23
Q
Does internal energy change when there is a change of state? Why?
A
Yes, because the potential energy of the particles is increased.
24
Q
Define specific heat capacity.
A
The amount of energy needed to raise the temperature of 1kg of a substance by 1K (or 1 degree C).
25
What is the symbol for specific heat capacity?
c
26
What are the units for specific heat capacity?
J/kg/K or J/kg/°C
27
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)
```
28
What is the unit for the mass used in the specific heat capacity equation?
kg
29
How can you investigate the effect on temperature by changing:
Mass?
Type of material (=changes specific heat capacity)?
Rate of energy transfer?
30
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.
31
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.
32
What technique can be used to measure specific heat capacity?
Using a continuous-flow calorimeter.
33
What is continuous-flow heating?
When a fluid flows continuously over a heating element, so energy is transferred to it.
34
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
35
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.
36
Define specific latent heat.
The quantity of thermal energy require to change the state of 1kg of a substance.
37
What is the unit for specific latent heat?
J/kg
38
Give the equation for the energy change relative to specific latent heat.
Q = ml
Where:
• m = Mass (kg)
• l = Specific latent heat (J/kg)
39
What unit for mass is used in specific latent heat calculations?
kg
40
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
41
What is the symbols for specific latent heat?
l
42
What is the lowest possible temperature called?
Absolute zero
43
What is absolute zero?
* The lowest possible temperature, where particles have the minimum possible kinetic energy
* 0K
44
How is the temperature is Kelvin related to the particle’s energy?
They are directly proportional.
45
How does the increment on the Kelvin scale differ from the Celsius scale?
They are the same (so 1K = 1°C).
46
Give the equation linking Kelvin and Celsius.
K = C + 273
47
What is the temperature of absolute zero in Kelvin and Celsius?
* 0K
| * -273°C
48
Give 100°C in Kelvin.
373K
49
Give 0°C in Kelvin.
273K
50
Which temperature scale is used in thermal physics?
Kelvin
51
What are the three gas laws and their equations?
* Boyle’s Law -> pV = constant
* Charles’ Law -> V/T = constant
* Pressure Law -> p/T = constant
52
What is an assumption of the 3 gas laws?
The mass of the gas is constant.
53
What is Boyle’s Law?
* pV = Constant
| * At a constant temperature, the pressure and volume of a gas are inversely proportional
54
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.
55
How does temperature affect the graph for Boyle’s Law (p-V)?
The higher the temperature, the further the curve is from the origin.
56
Why does Boyles Law happen (particles)?
If you reduce the volume, the particles will be closer together and collide more often = pressure increases
57
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.
58
What is Charles’ Law?
* V/T = Constant
| * At a constant pressure, the volume of a gas is directly proportional to its absolute temperature
59
Describe the graph for Charles’ Law.
* Volume against temperature plotted
* Straight line with positive gradient
* x-intercept is at -273°C or 0K
60
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
61
What is the Pressure Law?
* p/T = Constant
| * At a constant volume, the pressure of a gas is directly proportional to the temperature
62
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
63
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
64
What is an ideal gas?
One that obeys all 3 gas laws.
65
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.
66
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.
67
Remember to practise drawing out the setup for the gas law experiments.
Pg 111 of revision guide
68
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.
69
What is the relative mass of carbon-12?
12
70
What is the relative molecular mass of carbon dioxide? (1 carbon-12 molecule and 2 oxygen-16 molecules)
12 + 16 + 16 = 44
71
What is the molar mass of a gas?
The mass of one mole of that gas, usually in grams
72
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)
73
What is the symbol for Avogadro’s constant?
NA (where A is in subscript)
74
What can be said about the molar mass and the relative molecular mass?
They are the same value.
75
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.
76
What is the symbol for the number of moles?
n
77
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
78
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)
```
79
How is the ideal gas equation formed?
By combining the 3 gas laws.
80
What units for pressure, volume and temperature are used in the ideal gas equation?
* Pressure -> Pa
* Volume -> m³
* Temperature -> K
81
When does the ideal gas equation work best?
At low pressures and fairly high temperatures.
82
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)
83
What is the symbol for Boltzmann’s constant?
k
84
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
85
What is the value of Boltzmann’s constant?
1.38 x 10⁻²³ J/K
86
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)
```
87
What are the two equations for gases?
* Ideal gas equation -> pV = nRT
| * Equation of state -> pV = NkT
88
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.
89
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
90
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.)
91
How can the work done to expand a gas be found using a p-V graph?
It is the area under the graph.
92
Fill in the blanks
93
Write out how to derive the equations for the pressure of an ideal gas.
Pg 114 of revision guide
94
IMPORTANT: Remember to practise deriving the equations for the pressure of an ideal gas.
Pg 114 of revision guide
95
How do you derive the equation of the pressure of a single particle in an ideal gas?
96
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?
97
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
98
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!)
99
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)
100
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)
```
101
What does c²(bar) symbolise?
* Mean square speed
| * It is the average of the square speeds of all of the particles
102
What is the root mean square speed?
* The root of c²(bar)
| * It is a measure of the typical speed of a particle
103
What is the symbol for the root mean square speed?
c(rms)
| Where rms is subscript
104
Give the equation that links the rms speed and the mean square speed.
r.m.s. speed = √(mean square speed)
√ c²(bar) = c(rms)
105
What are the units for the root mean square speed?
m/s
106
What are the two important speeds in ideal gas equations?
* Mean square speed
| * r.m.s speed
107
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)
108
What are the simplified kinetic theory assumptions and how do you remember it?
109
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
110
Why is the potential energy of an ideal gas 0?
There are no forces between particles except when they are colliding.
111
When do real gases behave like ideal gases?
When the pressure is low and the temperature is high.
112
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.
113
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.
114
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
```
115
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)
116
How is the average kinetic energy of a gas related to the absolute temperature?
It is proportional.
117
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.
118
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
119
What are empirical laws?
Laws based on observation and evidence, without any explanation why.
120
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.
121
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.
122
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
123
For an ideal gas, internal energy = ?
Kinetic energy of atoms
124
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.
125
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
126
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
127
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.
128
Why can’t scientific ideas be accepted immediately?
The ideas have to be independently validated or anyone could just make up any nonsense.
129
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.
130
What is kinetic theory?
The body of theory that explains the physical properties of matter in terms of the motion of its particles.
131
Who and when discovered Brownian motion?
Robert Brown in 1827
132
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)
133
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.
134
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.
135
Why does Boyles Law happen (particles)?
If you reduce the volume, the particles will be closer together and collide more often = pressure increases.
