Thermodynamic system
The concept (thermodynamic) system as used in this book refers to that part of the world
whose thermodynamic properties are the subject of our interest, while the term surroundings
is used for the remaining part of the universe.
Note: Both a certain part of the real space and a certain part of the imaginary (abstract)
space forming a simplified model system, e.g. an ideal gas, may be chosen as a system.
Systems are classified as isolated, closed and open, based on their inter-relations with their
surroundings.
The concept (thermodynamic) system as used in this book refers to that part of the world
whose thermodynamic properties are the subject of our interest, while the term surroundings
is used for the remaining part of the universe.
Note: Both a certain part of the real space and a certain part of the imaginary (abstract)
space forming a simplified model system, e.g. an ideal gas, may be chosen as a system.
Systems are classified as isolated, closed and open, based on their inter-relations with their
surroundings.
Isolated system
A chemical system exchanging neither matter nor energy with its surroundings is an isolated
system.
A chemical system exchanging neither matter nor energy with its surroundings is an isolated
system.
Closed system
A chemical system exchanging energy but not matter with its surroundings is a closed system.
A chemical system exchanging energy but not matter with its surroundings is a closed system.
Open system
A chemical system exchanging both energy and matter with its surroundings is an open system.
Example
Differences between individual types of chemical systems may be demonstrated using the example
of making coffee. The pot on the heater represents a (practically) closed system until the water
is brought to the boil. At the boiling point, when steam is leaking from the pot, it becomes an
open system. The ready-made coffee kept in a thermos bottle represents a simple model of an
isolated system.
A chemical system exchanging both energy and matter with its surroundings is an open system.
Example
Differences between individual types of chemical systems may be demonstrated using the example
of making coffee. The pot on the heater represents a (practically) closed system until the water
is brought to the boil. At the boiling point, when steam is leaking from the pot, it becomes an
open system. The ready-made coffee kept in a thermos bottle represents a simple model of an
isolated system.
Phase, homogeneous and heterogeneous systems
The term phase is used for that portion of the investigated system volume in which its properties
are constant or continuously changing in space. If a system behaves in this way throughout
all its volume, we call it a homogeneous system. If a system contains more phases, we call
it a heterogeneous system.
Example
Let us imagine a bottle of whisky. How many phases does this system consist of?
The term phase is used for that portion of the investigated system volume in which its properties
are constant or continuously changing in space. If a system behaves in this way throughout
all its volume, we call it a homogeneous system. If a system contains more phases, we call
it a heterogeneous system.
Example
Let us imagine a bottle of whisky. How many phases does this system consist of?
Solution
If we are, from the thermodynamic point of view, interested solely in the liquid content of the
bottle, the system is homogeneous. It contains one liquid phase (a mixture of water, ethanol and
some additives). If, on the other hand, we are interested in the entire content of the bottle but
not the bottle itself, the system is heterogeneous. In this case it consists of two phases, liquid and
gaseous, with the latter containing air and whisky vapour. If, however, we focus our attention
on both the bottle content and the bottle itself, we have a heterogeneous system again, but this
time it also contains other phases in addition to the gaseous and liquid ones, i.e. the glass of the
bottle, its cap, label, etc.
If we are, from the thermodynamic point of view, interested solely in the liquid content of the
bottle, the system is homogeneous. It contains one liquid phase (a mixture of water, ethanol and
some additives). If, on the other hand, we are interested in the entire content of the bottle but
not the bottle itself, the system is heterogeneous. In this case it consists of two phases, liquid and
gaseous, with the latter containing air and whisky vapour. If, however, we focus our attention
on both the bottle content and the bottle itself, we have a heterogeneous system again, but this
time it also contains other phases in addition to the gaseous and liquid ones, i.e. the glass of the
bottle, its cap, label, etc.
The volume of a system as an extensive quantity. The volume V is the sum of the volumes
of the individual parts (i.e. sub-systems) I, II and III, i.e. V = VI + VII + VIII.
of the individual parts (i.e. sub-systems) I, II and III, i.e. V = VI + VII + VIII.
Energy
There are two basic forms of energy exchange between a system and its surroundings, heat
and work. A positive value is assigned to such energy exchange during which the system gains
energy (work or heat) from its surroundings, i.e. energy is added to the system. A negative
value indicates that the system passes energy (work or heat) to its surroundings, i.e. energy is
subtracted from the system.
There are two basic forms of energy exchange between a system and its surroundings, heat
and work. A positive value is assigned to such energy exchange during which the system gains
energy (work or heat) from its surroundings, i.e. energy is added to the system. A negative
value indicates that the system passes energy (work or heat) to its surroundings, i.e. energy is
subtracted from the system.
Heat
When the energy of a system changes as a result of a temperature difference between the system
and its surroundings (e.g. transfer of kinetic energy of disordered movement of molecules), we
speak about exchanged heat.
When the energy of a system changes as a result of a temperature difference between the system
and its surroundings (e.g. transfer of kinetic energy of disordered movement of molecules), we
speak about exchanged heat.
Work
Other forms of energy exchange, which are usually driven by some forces acting between the
system and its surroundings, are called work. Based on the type of interaction between the
system and its surroundings, we distinguish volume work [see 3.1.2], electrical work, surface
work, etc.
Other forms of energy exchange, which are usually driven by some forces acting between the
system and its surroundings, are called work. Based on the type of interaction between the
system and its surroundings, we distinguish volume work [see 3.1.2], electrical work, surface
work, etc.
Thermodynamic quantities
Observation of any system allows us to determine a number of its properties. The properties
in which we are interested from the thermodynamic point of view are called thermodynamic
quantities, or, briefly, quantities. Typical thermodynamic quantities are temperature,
pressure, volume, enthalpy and entropy. Neither heat nor work rank among thermodynamic
quantities.
Note: Terms such as thermodynamic function, thermodynamic variable, state quantity
(i.e. a quantity determining the state of a system, see 1.4), state function, or state variable
are used as synonyms of the term thermodynamic quantity.
Observation of any system allows us to determine a number of its properties. The properties
in which we are interested from the thermodynamic point of view are called thermodynamic
quantities, or, briefly, quantities. Typical thermodynamic quantities are temperature,
pressure, volume, enthalpy and entropy. Neither heat nor work rank among thermodynamic
quantities.
Note: Terms such as thermodynamic function, thermodynamic variable, state quantity
(i.e. a quantity determining the state of a system, see 1.4), state function, or state variable
are used as synonyms of the term thermodynamic quantity.
Intensive and extensive thermodynamic quantities
Let us consider a homogeneous system without any external force fields present. We distinguish
between extensive and intensive thermodynamic quantities of a system. Intensive quantities
are those whose values do not change when the system is divided into smaller sub-systems.
Extensive quantities are those whose values are proportional to the amount of substance of
the system at a fixed temperature and pressure (see Figure 1.1). Temperature, pressure, and
composition expressed by mole fractions are typical intensive quantities. Volume, mass and the
number of particles are typical extensive quantities.
Note: Some quantities, e.g. the system surface, are neither extensive nor intensive.
Every extensive quantity may be converted into an intensive one if we relate it to a certain
constant mass of the system. We then obtain specific or molar quantities (see 3.2.5). For every
extensive quantity X and the respective molar and specific quantities Xm and x we may
write
X = nXm , (1.1)
X = mx , (1.2)
Let us consider a homogeneous system without any external force fields present. We distinguish
between extensive and intensive thermodynamic quantities of a system. Intensive quantities
are those whose values do not change when the system is divided into smaller sub-systems.
Extensive quantities are those whose values are proportional to the amount of substance of
the system at a fixed temperature and pressure (see Figure 1.1). Temperature, pressure, and
composition expressed by mole fractions are typical intensive quantities. Volume, mass and the
number of particles are typical extensive quantities.
Note: Some quantities, e.g. the system surface, are neither extensive nor intensive.
Every extensive quantity may be converted into an intensive one if we relate it to a certain
constant mass of the system. We then obtain specific or molar quantities (see 3.2.5). For every
extensive quantity X and the respective molar and specific quantities Xm and x we may
write
X = nXm , (1.1)
X = mx , (1.2)
where n is the amount of substance and m is the mass of the system.
We will use the subscript m to denote molar quantities and small letters to denote
specific quantities.
specific quantities.
The state of a system and its changes
Any system may be in any moment characterized using a certain number of quantities. These
quantities define the state of a given system. The degree of generality at which we observe
a given system has to be taken into account at the same time. In terms of a microscopic
scale, the state of a system is defined by the position and velocity of all its particles. In terms
of thermodynamics, however, it is enough to know only a few quantities, e.g. temperature,
pressure and composition.
Any system may be in any moment characterized using a certain number of quantities. These
quantities define the state of a given system. The degree of generality at which we observe
a given system has to be taken into account at the same time. In terms of a microscopic
scale, the state of a system is defined by the position and velocity of all its particles. In terms
of thermodynamics, however, it is enough to know only a few quantities, e.g. temperature,
pressure and composition.
The state of thermodynamic equilibrium
The state of thermodynamic equilibrium (equilibrium state, equilibrium) is a state in which no
macroscopic changes occur in the system and all quantities have constant values in time.
Note: In the state of thermodynamic equilibrium, changes take place at the microscopic
level. For instance, when the liquid and vapour phases are in equilibrium, some molecules
continuously move from the liquid to the vapour phase and others from the vapour to the
liquid phase. However, the temperature and pressure of the system do not change.
The state of thermodynamic equilibrium embraces the following partial equilibria:
• mechanical (pressure) equilibrium—the pressure in all parts of the system is the same 1,
• thermal (temperature) equilibrium—the temperature in all parts of the system is equalized,
• concentration equilibrium—the concentration of the system components is the same in
all parts of each phase of the system, but the composition of individual phases is usually
different,
• chemical equilibrium—no changes in composition occur as a result of chemical reactions,
• phase equilibrium—if a system is heterogeneous (see 1.1.4), the components of its phases
are in equilibrium.
The state of thermodynamic equilibrium (equilibrium state, equilibrium) is a state in which no
macroscopic changes occur in the system and all quantities have constant values in time.
Note: In the state of thermodynamic equilibrium, changes take place at the microscopic
level. For instance, when the liquid and vapour phases are in equilibrium, some molecules
continuously move from the liquid to the vapour phase and others from the vapour to the
liquid phase. However, the temperature and pressure of the system do not change.
The state of thermodynamic equilibrium embraces the following partial equilibria:
• mechanical (pressure) equilibrium—the pressure in all parts of the system is the same 1,
• thermal (temperature) equilibrium—the temperature in all parts of the system is equalized,
• concentration equilibrium—the concentration of the system components is the same in
all parts of each phase of the system, but the composition of individual phases is usually
different,
• chemical equilibrium—no changes in composition occur as a result of chemical reactions,
• phase equilibrium—if a system is heterogeneous (see 1.1.4), the components of its phases
are in equilibrium.
Note: If a system in the state of thermodynamic equilibrium occurs in an external force
field, e.g. the gravitational field, the pressure is not the same in all parts of the system
but it changes continuously. The concentration of the system components also changes
continuously in each phase, with a discontinual change occurring at the phase boundary.
field, e.g. the gravitational field, the pressure is not the same in all parts of the system
but it changes continuously. The concentration of the system components also changes
continuously in each phase, with a discontinual change occurring at the phase boundary.
System’s transition to the state of equilibrium
If a system is not in the state of equilibrium, its properties change in time in such a way that
it tends toward equilibrium. Thermodynamics postulates that every system under invariable
external conditions is bound to attain the state of thermodynamic equilibrium. The time needed
for a system to attain equilibrium varies considerably, ranging from fractions of a second needed
for pressure equalization up to hundreds of years needed for glass transition to the crystalline
state. A measure of the velocity of a system’s transition to equilibrium is called the relaxation
time.
Example
If we immerse several crystals of copper(II) sulphate pentahydrate (CuSO4·5H2O) into a closed
vessel containing water, the system thus created will be in a non-equilibrium state at the beginning.
There will be neither a phase equilibrium between the crystals and the liquid phase
nor a concentration equilibrium. After some time the crystals will dissolve (phase equilibrium).
If we do not mix the system, the dissolved copper(II) sulphate pentahydrate will slowly diffuse
through the solution from the bottom up to the surface, and after many weeks (relaxation time),
concentration in all parts of the system will become equal as well (thermodynamic equilibrium).
If a system is not in the state of equilibrium, its properties change in time in such a way that
it tends toward equilibrium. Thermodynamics postulates that every system under invariable
external conditions is bound to attain the state of thermodynamic equilibrium. The time needed
for a system to attain equilibrium varies considerably, ranging from fractions of a second needed
for pressure equalization up to hundreds of years needed for glass transition to the crystalline
state. A measure of the velocity of a system’s transition to equilibrium is called the relaxation
time.
Example
If we immerse several crystals of copper(II) sulphate pentahydrate (CuSO4·5H2O) into a closed
vessel containing water, the system thus created will be in a non-equilibrium state at the beginning.
There will be neither a phase equilibrium between the crystals and the liquid phase
nor a concentration equilibrium. After some time the crystals will dissolve (phase equilibrium).
If we do not mix the system, the dissolved copper(II) sulphate pentahydrate will slowly diffuse
through the solution from the bottom up to the surface, and after many weeks (relaxation time),
concentration in all parts of the system will become equal as well (thermodynamic equilibrium).
Thermodynamic process
If the properties of a system change in time, i.e. if at least one thermodynamic quantity changes,
we say that a certain thermodynamic process takes place in the system. The term process
relates to a very broad range of most varied processes, from simple physical changes such as,
e.g., heating, various chemical reactions, up to complex multistage processes. Individual kinds
of processes may be classified according to several criteria.
If the properties of a system change in time, i.e. if at least one thermodynamic quantity changes,
we say that a certain thermodynamic process takes place in the system. The term process
relates to a very broad range of most varied processes, from simple physical changes such as,
e.g., heating, various chemical reactions, up to complex multistage processes. Individual kinds
of processes may be classified according to several criteria.
Reversible and irreversible processes
The course of any process depends on the conditions under which the given system changes.
If we arrange the conditions in such a way that the system is nearly at equilibrium in every
moment, and that, consequently, the direction of the process may be reversed by even a very
slight change of the initial conditions, the process is called reversible or equilibrium. A
reversible process is thus a sequence of (nearly) equilibrium states of a system.
However, processes in the real world are mostly such that the system is out of equilibrium
at least at the beginning. These processes are called irreversible or non-equilibrium (the
direction of the process cannot be reversed by any slight change of external conditions, and
the process is a sequence of non-equilibrium states). An equilibrium process is thus actually a
limiting case of a non-equilibrium process going on at an infinitesimal velocity.
Example
Infinitely slow heating or infinitely slow compression of a system may serve as an example of
equilibrium processes which cannot be carried out in practice. In contrast, water boiling at a
temperature of 100 C and pressure of 101 325 Pa is an example of an equilibrium process which
may take place in practice. If we lower the temperature slightly, the direction of the process will
be reversed and boiling will be replaced by water vapour condensation.
The course of any process depends on the conditions under which the given system changes.
If we arrange the conditions in such a way that the system is nearly at equilibrium in every
moment, and that, consequently, the direction of the process may be reversed by even a very
slight change of the initial conditions, the process is called reversible or equilibrium. A
reversible process is thus a sequence of (nearly) equilibrium states of a system.
However, processes in the real world are mostly such that the system is out of equilibrium
at least at the beginning. These processes are called irreversible or non-equilibrium (the
direction of the process cannot be reversed by any slight change of external conditions, and
the process is a sequence of non-equilibrium states). An equilibrium process is thus actually a
limiting case of a non-equilibrium process going on at an infinitesimal velocity.
Example
Infinitely slow heating or infinitely slow compression of a system may serve as an example of
equilibrium processes which cannot be carried out in practice. In contrast, water boiling at a
temperature of 100 C and pressure of 101 325 Pa is an example of an equilibrium process which
may take place in practice. If we lower the temperature slightly, the direction of the process will
be reversed and boiling will be replaced by water vapour condensation.
Processes at a constant quantity
In most investigated processes, one or more thermodynamic quantities are maintained constant
during the whole process. These processes are mostly termed using the prefix iso- (is-), and
denoted using the symbol [X], with X indicating the given constant quantity. The following
processes are encountered most often:
In most investigated processes, one or more thermodynamic quantities are maintained constant
during the whole process. These processes are mostly termed using the prefix iso- (is-), and
denoted using the symbol [X], with X indicating the given constant quantity. The following
processes are encountered most often:
Name of the process Constant quantity Symbol
Isothermal temperature [T]
Isobaric pressure [p]
Isochoric volume [V ]
Adiabatic heat [ad]
Isentropic entropy [S]
Isenthalpic enthalpy [H]
Polytropic heat capacity [C]
Isothermal temperature [T]
Isobaric pressure [p]
Isochoric volume [V ]
Adiabatic heat [ad]
Isentropic entropy [S]
Isenthalpic enthalpy [H]
Polytropic heat capacity [C]
Example
In the initial state, a system of a constant volume has a temperature of 300K and a pressure
of 150 kPa. A certain process takes place in the system, and in the final state the system’s
temperature is 320K and its pressure is 150 kPa. Does the process take place under a constant
thermodynamic quantity?
Solution
The initial and the final temperatures of the system are different. Consequently, the process
cannot be isothermal. Both the initial pressure and the final pressure are identical. In this case
it may be, but not necessarily is, an isobaric process. The specification does not allow us to find
out whether pressure changes in any way in the course of the process. However, the process is
definitely an isochoric one because the system has a constant (i.e. unchanging) volume.
In the initial state, a system of a constant volume has a temperature of 300K and a pressure
of 150 kPa. A certain process takes place in the system, and in the final state the system’s
temperature is 320K and its pressure is 150 kPa. Does the process take place under a constant
thermodynamic quantity?
Solution
The initial and the final temperatures of the system are different. Consequently, the process
cannot be isothermal. Both the initial pressure and the final pressure are identical. In this case
it may be, but not necessarily is, an isobaric process. The specification does not allow us to find
out whether pressure changes in any way in the course of the process. However, the process is
definitely an isochoric one because the system has a constant (i.e. unchanging) volume.
Cyclic process
A cyclic process is such at which the final state of the system is identical with its initial state.
In a cyclic process, changes of thermodynamic quantities are zero.
Note: Heat and work are not thermodynamic quantities and therefore they are not zero
during a cyclic process.
A cyclic process is such at which the final state of the system is identical with its initial state.
In a cyclic process, changes of thermodynamic quantities are zero.
Note: Heat and work are not thermodynamic quantities and therefore they are not zero
during a cyclic process.
Example
Let our system be a cube of ice with a mass of 1 g, and the initial state be a temperature of
−10 C and a pressure of 100 kPa. The sequence of processes taking place in the system was as
follows: the cube was heated to 0 C at which it melted. The liquid water was electrolyzed at this
temperature. The resulting mixture of hydrogen and oxygen was expanded to 200 Pa and ignited.
The water vapour resulting from the reaction had a temperature of 500 C at the end of the
reaction. It was then cooled to −10 C and compressed to 100 kPa. In the course of compression
desublimation (snowing) occurred, and the system returned to its initial thermodynamic state. A
cyclic process took place.
Let our system be a cube of ice with a mass of 1 g, and the initial state be a temperature of
−10 C and a pressure of 100 kPa. The sequence of processes taking place in the system was as
follows: the cube was heated to 0 C at which it melted. The liquid water was electrolyzed at this
temperature. The resulting mixture of hydrogen and oxygen was expanded to 200 Pa and ignited.
The water vapour resulting from the reaction had a temperature of 500 C at the end of the
reaction. It was then cooled to −10 C and compressed to 100 kPa. In the course of compression
desublimation (snowing) occurred, and the system returned to its initial thermodynamic state. A
cyclic process took place.
