Thermodynamics (Oct-Dec 2023) Course Outline
Thermodynamics
Course Outline
Prof Carl Paterson
(Blackett 607, )
Thermodynamics forms the central part of the Thermal Physics and Structure of Matter
module. Thermodynamics is one of the pillars of physics. It is a macroscopic, self-contained
system that is built upon a few, well-defined physics principles — the laws of thermodynam-
ics — but which provides an incredibly powerful and compact framework to understand,
analyse and predict behaviour of physical systems.
In this part of the module, we will focus primarily on learning outcomes 3 and 4 in the
module description:
3. Demonstrate an appreciation and understanding of the zeroth, first and third laws of
thermodynamics and their applicability and generality across physics.
4. State the various forms of the second law of thermodynamics, show the equivalence
between them and describe how the law highlights a fundamental asymmetry in na-
ture.
These are quite broad. In more detail, you should:
• know the four laws of thermodynamics
• understand thermodynamics as a macroscopic theory that exists independently of micro-
scopic theories of matter
• understand the ideas of thermodynamic systems
• understand concepts of temperature and entropy and appreciate and use their varied
definitions
• be able to use equations of state to predict properties of thermodynamic systems
• understand and be able to use the concept of thermodynamic equilibrium
• understand the concepts of work, heat, internal energy and their relationship via the first
law
• be able to describe and analyse thermodynamic processes with the use of PV and TS
diagrams
• understand the concept of thermodynamic cycles and be able to use them to derive
efficiencies and performances of heat engines, heat pumps and refrigerators
• know that the second law can be stated in alternative forms and be able to show their
equivalence
• understand concepts of reversible, irreversible and quasistatic processes
• describe the Carnot cycle and show that it is the most efficient cycle possible between
two heat reservoirs
• generalize the Carnot cycle to systems other than ideal gases
• understand how thermodynamic entropy arises from the second law
• understand the concept of an asymmetry in time arising from the second law and the
concept of energy degradation
• appreciate the importance of derived thermodynamic potentials for different external con-
straints
• be able to derive and use Maxwell relations to calculate changes in temperature, volume,
pressure and entropy
• appreciate differences in states and phases of matter and be able to to use PV and PT
diagrams to describe phase changes
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,Thermodynamics (Oct-Dec 2023) Course Outline
• understand and be able to use the Clausius–Clapeyron relation to compute behaviour
and shifts in melting and boiling points
• understand and describe behaviour of non-ideal gases under different types of expan-
sions and the consequent temperature changes
• understand the use of chemical potential for systems and phase changes
• know that the third law can be stated in various forms and understand how they relate to
unattainability of absolute zero
• understand implications of the third law on thermodynamic properties as systems ap-
proache absolute zero
We will make use of and link to the other parts of the module. In particular, we will use
of some of the earlier parts from the structure of matter lectures. The statistical physics
lectures later in the module will build on the thermodynamics we cover here.
Notes and problems
Summary notes (available on Blackboard) will contain the essential derivations and defini-
tions that you will need. They will not contain all the wider discussion that we will cover in the
lectures or seminars. It is recommended that you supplement with your own notes or anno-
tations. The act of selective note-taking, or note-making can help both with understanding
of and later recalling of ideas discussed.
Doing problems is a core part of the course. Some of the ideas and material in the course
will be covered in the problems but will not be discussed in detail in the lectures.
Lecture Outline
Thermodynamic processes and concepts (L1-5)
• thermodynamics as a macroscopic theory
• basic concepts, equilibrium and state
• internal energy, temperature, entropy
• the first law of thermodynamics
• expansions and compressions of gases
The second law (L6-10)
• reversibility, heat engines, heat pumps and refrigerators
• the second law of thermodynamics
• Carnot cycles and Carnot’s theorem
• entropy and the Clausius inequality
Using thermodynamics (L11-18)
• thermodynamic potentials and Maxwell relations
• adiabatic expansions of real gases
• chemical potential
• phase transitions
• Clausius–Clapeyron relation and phase changes
• generalized variables
• the third law
• entropy and the arrow of time
2 of 2
,Thermodynamics (Oct-Dec 2023) Outline Notes: Lecture 1
Outline Notes: Lecture 1
1 Basic concepts and definitions
1.1 Systems and surroundings
In thermodynamics we divide the problem into a system and its surroundings.
System: The thing/object/entity we are interested in. This might be a gas in a container.
Surroundings: The external environment that the system can interact with.
Systems can interact (or not) with the surroundings in a variety of ways:
Isolated system: The energy and matter in the system is fixed. There is no exchange of
energy with the surroundings. An example would be a fixed volume of gas in a rigid
container that is thermally insulating.
Closed system: The system may be able to exchange energy with the surroundings, but
not matter. For example this might be a gas in a container. A common closed system
that we will make much use of will be gas in a cylinder with a moveable piston. Energy
can enter or leave the system by doing work on the piston, or by heat flowing through
the walls.
Open system: The system may be able to exchange both energy and matter with the
surroundings. An example might be the gas in a particular volume of space where
molecules and heat are free to enter and leave the volume.
The division between system and surroundings can be arbitrary. We choose what to con-
sider as the system and what to consider as the surroundings depending on what aspects
of the physics we are interested in investigating.
1.2 State variables
Thermodynamics is a macroscopic theory. We use macroscopic properties to describe the
state of a system. These are intrinsic properties representing the interior of the system as
a whole.
Examples: for a gas, state variables include pressure (P), volume (V), temperature (T ),
number of molecules (N).
State variables are sometimes called functions of state. State variables depend only on the
current state of the system. In principle we can measure the values of the state variables
from the current state of the system without knowing its history.
If a system goes through a series of changes and returns to its initial state, the state vari-
ables will return to the same values.
System variables can be extensive or intensive.
Extensive variables: These are properties that are proportional to the size (or amount) of
material (V, N, etc.)
1 of 3
, Thermodynamics (Oct-Dec 2023) Outline Notes: Lecture 1
Intensive variables: These are properties that are independent of the amount of material
(e.g., P, T ).
For example if we take two identical containers of gas each described by variables P, V, T , N
and combine them, the resulting gas will be described by state variables P, 2V, T , 2N. The
extensive variables have doubled with the amount of gas V, N ! 2V, 2N. The intensive
variables T , P are unchanged.
Specific values For many extensive quantities we can define a corresponding specific
value by dividing by the amount of material. We can divide by mass, volume, number of
moles, depending on the problem. Specific values are usually denoted with a lower-case
letter of the corresponding macroscopic variable. E.g., for a system with a heat capacity CV
we can obtain a specific heat capacity (per unit mass) cv = Cv /m. In chemistry it is often
useful to have specific values per mole of a quantity (i.e., molar values).
For a system in thermodynamic equilibrium, the state variables are constant and unchang-
ing and usually well-defined.
Intensive variables usually correspond to an internal material property that can in principle
take a value at each point. Intensive state variables are uniform throughout the system for a
system in thermodynamic equilibrium, but may not be when the system is not in equilibrium.
For example, the temperature of a system is only well defined for a system in thermal
equilibrium.
Extensive state variables are usually well defined throughout a process, including when the
system is not equilibrium.
Different sets of state variables will be relevant for different systems - e.g., tension J and
extension L for a wire under tension; field B and magnetisation M for a magnetic material.
1.3 Equilibrium
Equilibrium is the state that the system will settle to if left alone. In equilibrium, the state
variables are static. Microscopically, the system may still be moving, e.g., the molecules in
a volume of gas. That is not important (or relevant) for our thermodynamic approach.
Mechanical equilibrium: A system is in mechanical equilibrium when the forces acting
upon it are in balance. For example a gas in a cylinder/piston at pressure P with
an external force F applied to the piston that balances the force from the internal
pressure of the gas.
Chemical equilibrium: The numbers Nj of the different species of molecule in a chemical
system are constant. This does not mean that molecules of a species are not entering
of leaving via chemical reactions, but there is no net change.
Thermal equilibrium: Temperature is well-defined for the system.
Thermodynamic equilibrium: mechanical, chemical and thermal equilibrium.
A system may have many equilibrium states. Different equilibrium states will be described
by different values of the state variables. For example if we add an amount of energy to
a volume of ideal gas and allow it to settle it will be in a different equilibrium state, with
2 of 3
Thermodynamics
Course Outline
Prof Carl Paterson
(Blackett 607, )
Thermodynamics forms the central part of the Thermal Physics and Structure of Matter
module. Thermodynamics is one of the pillars of physics. It is a macroscopic, self-contained
system that is built upon a few, well-defined physics principles — the laws of thermodynam-
ics — but which provides an incredibly powerful and compact framework to understand,
analyse and predict behaviour of physical systems.
In this part of the module, we will focus primarily on learning outcomes 3 and 4 in the
module description:
3. Demonstrate an appreciation and understanding of the zeroth, first and third laws of
thermodynamics and their applicability and generality across physics.
4. State the various forms of the second law of thermodynamics, show the equivalence
between them and describe how the law highlights a fundamental asymmetry in na-
ture.
These are quite broad. In more detail, you should:
• know the four laws of thermodynamics
• understand thermodynamics as a macroscopic theory that exists independently of micro-
scopic theories of matter
• understand the ideas of thermodynamic systems
• understand concepts of temperature and entropy and appreciate and use their varied
definitions
• be able to use equations of state to predict properties of thermodynamic systems
• understand and be able to use the concept of thermodynamic equilibrium
• understand the concepts of work, heat, internal energy and their relationship via the first
law
• be able to describe and analyse thermodynamic processes with the use of PV and TS
diagrams
• understand the concept of thermodynamic cycles and be able to use them to derive
efficiencies and performances of heat engines, heat pumps and refrigerators
• know that the second law can be stated in alternative forms and be able to show their
equivalence
• understand concepts of reversible, irreversible and quasistatic processes
• describe the Carnot cycle and show that it is the most efficient cycle possible between
two heat reservoirs
• generalize the Carnot cycle to systems other than ideal gases
• understand how thermodynamic entropy arises from the second law
• understand the concept of an asymmetry in time arising from the second law and the
concept of energy degradation
• appreciate the importance of derived thermodynamic potentials for different external con-
straints
• be able to derive and use Maxwell relations to calculate changes in temperature, volume,
pressure and entropy
• appreciate differences in states and phases of matter and be able to to use PV and PT
diagrams to describe phase changes
1 of 2
,Thermodynamics (Oct-Dec 2023) Course Outline
• understand and be able to use the Clausius–Clapeyron relation to compute behaviour
and shifts in melting and boiling points
• understand and describe behaviour of non-ideal gases under different types of expan-
sions and the consequent temperature changes
• understand the use of chemical potential for systems and phase changes
• know that the third law can be stated in various forms and understand how they relate to
unattainability of absolute zero
• understand implications of the third law on thermodynamic properties as systems ap-
proache absolute zero
We will make use of and link to the other parts of the module. In particular, we will use
of some of the earlier parts from the structure of matter lectures. The statistical physics
lectures later in the module will build on the thermodynamics we cover here.
Notes and problems
Summary notes (available on Blackboard) will contain the essential derivations and defini-
tions that you will need. They will not contain all the wider discussion that we will cover in the
lectures or seminars. It is recommended that you supplement with your own notes or anno-
tations. The act of selective note-taking, or note-making can help both with understanding
of and later recalling of ideas discussed.
Doing problems is a core part of the course. Some of the ideas and material in the course
will be covered in the problems but will not be discussed in detail in the lectures.
Lecture Outline
Thermodynamic processes and concepts (L1-5)
• thermodynamics as a macroscopic theory
• basic concepts, equilibrium and state
• internal energy, temperature, entropy
• the first law of thermodynamics
• expansions and compressions of gases
The second law (L6-10)
• reversibility, heat engines, heat pumps and refrigerators
• the second law of thermodynamics
• Carnot cycles and Carnot’s theorem
• entropy and the Clausius inequality
Using thermodynamics (L11-18)
• thermodynamic potentials and Maxwell relations
• adiabatic expansions of real gases
• chemical potential
• phase transitions
• Clausius–Clapeyron relation and phase changes
• generalized variables
• the third law
• entropy and the arrow of time
2 of 2
,Thermodynamics (Oct-Dec 2023) Outline Notes: Lecture 1
Outline Notes: Lecture 1
1 Basic concepts and definitions
1.1 Systems and surroundings
In thermodynamics we divide the problem into a system and its surroundings.
System: The thing/object/entity we are interested in. This might be a gas in a container.
Surroundings: The external environment that the system can interact with.
Systems can interact (or not) with the surroundings in a variety of ways:
Isolated system: The energy and matter in the system is fixed. There is no exchange of
energy with the surroundings. An example would be a fixed volume of gas in a rigid
container that is thermally insulating.
Closed system: The system may be able to exchange energy with the surroundings, but
not matter. For example this might be a gas in a container. A common closed system
that we will make much use of will be gas in a cylinder with a moveable piston. Energy
can enter or leave the system by doing work on the piston, or by heat flowing through
the walls.
Open system: The system may be able to exchange both energy and matter with the
surroundings. An example might be the gas in a particular volume of space where
molecules and heat are free to enter and leave the volume.
The division between system and surroundings can be arbitrary. We choose what to con-
sider as the system and what to consider as the surroundings depending on what aspects
of the physics we are interested in investigating.
1.2 State variables
Thermodynamics is a macroscopic theory. We use macroscopic properties to describe the
state of a system. These are intrinsic properties representing the interior of the system as
a whole.
Examples: for a gas, state variables include pressure (P), volume (V), temperature (T ),
number of molecules (N).
State variables are sometimes called functions of state. State variables depend only on the
current state of the system. In principle we can measure the values of the state variables
from the current state of the system without knowing its history.
If a system goes through a series of changes and returns to its initial state, the state vari-
ables will return to the same values.
System variables can be extensive or intensive.
Extensive variables: These are properties that are proportional to the size (or amount) of
material (V, N, etc.)
1 of 3
, Thermodynamics (Oct-Dec 2023) Outline Notes: Lecture 1
Intensive variables: These are properties that are independent of the amount of material
(e.g., P, T ).
For example if we take two identical containers of gas each described by variables P, V, T , N
and combine them, the resulting gas will be described by state variables P, 2V, T , 2N. The
extensive variables have doubled with the amount of gas V, N ! 2V, 2N. The intensive
variables T , P are unchanged.
Specific values For many extensive quantities we can define a corresponding specific
value by dividing by the amount of material. We can divide by mass, volume, number of
moles, depending on the problem. Specific values are usually denoted with a lower-case
letter of the corresponding macroscopic variable. E.g., for a system with a heat capacity CV
we can obtain a specific heat capacity (per unit mass) cv = Cv /m. In chemistry it is often
useful to have specific values per mole of a quantity (i.e., molar values).
For a system in thermodynamic equilibrium, the state variables are constant and unchang-
ing and usually well-defined.
Intensive variables usually correspond to an internal material property that can in principle
take a value at each point. Intensive state variables are uniform throughout the system for a
system in thermodynamic equilibrium, but may not be when the system is not in equilibrium.
For example, the temperature of a system is only well defined for a system in thermal
equilibrium.
Extensive state variables are usually well defined throughout a process, including when the
system is not equilibrium.
Different sets of state variables will be relevant for different systems - e.g., tension J and
extension L for a wire under tension; field B and magnetisation M for a magnetic material.
1.3 Equilibrium
Equilibrium is the state that the system will settle to if left alone. In equilibrium, the state
variables are static. Microscopically, the system may still be moving, e.g., the molecules in
a volume of gas. That is not important (or relevant) for our thermodynamic approach.
Mechanical equilibrium: A system is in mechanical equilibrium when the forces acting
upon it are in balance. For example a gas in a cylinder/piston at pressure P with
an external force F applied to the piston that balances the force from the internal
pressure of the gas.
Chemical equilibrium: The numbers Nj of the different species of molecule in a chemical
system are constant. This does not mean that molecules of a species are not entering
of leaving via chemical reactions, but there is no net change.
Thermal equilibrium: Temperature is well-defined for the system.
Thermodynamic equilibrium: mechanical, chemical and thermal equilibrium.
A system may have many equilibrium states. Different equilibrium states will be described
by different values of the state variables. For example if we add an amount of energy to
a volume of ideal gas and allow it to settle it will be in a different equilibrium state, with
2 of 3
