Thermodynamics
From Wikipedia, the free encyclopedia
In physics, thermodynamics (from the Greek θέρμη therme, meaning
"heat"[1] and δύναμις, dynamis, meaning "power") is the study of energy conversion between
heat and mechanical work, and subsequently the macroscopic variables such
as temperature, volume and pressure. Its progenitor, based on statistical predictions of the
collective motion of particles from their microscopic behavior, is the field of statistical
thermodynamics (or statistical mechanics), a branch of statistical physics.[2][3][4] Historically,
thermodynamics developed out of need to increase the efficiency of early steam engines.[5]
Typical thermodynamic system, showing input from a heat source (boiler) on the left and output to a heat sink
(condenser) on the right. Work is extracted, in this case by a series of pistons.
Contents
[show]
[edit]Introduction
Thermodynamic equations
Laws of thermodynamics
Conjugate variables
Thermodynamic potential
Material properties
Maxwell relations
Bridgman's equations
Exact differential
Table of thermodynamic equations
edit
The starting point for most thermodynamic considerations are the laws of thermodynamics,
which postulate that energy can be exchanged between physical systems as heat
or work.[6] They also postulate the existence of a quantity namedentropy, which can be defined
for any isolated system that is in thermodynamic equilibrium.[7] In thermodynamics, interactions
between large ensembles of objects are studied and categorized. Central to this are the
concepts of system andsurroundings. A system is composed of particles, whose average
motions define its properties, which in turn are related to one another through equations of
state. Properties can be combined to express internal energy and thermodynamic potentials,
which are useful for determining conditions for equilibrium andspontaneous processes.
With these tools, the usage of thermodynamics describes how systems respond to changes in
their surroundings. This can be applied to a wide variety of topics inscience and engineering,
such as engines, phase transitions, chemical reactions, transport phenomena, and even black
holes. The results of thermodynamics are essential for other fields of physics and
forchemistry, chemical engineering, aerospace engineering, mechanical engineering, cell
biology,biomedical engineering, materials science, and economics to name a few.[8][9]
[edit]Developments
Sadi Carnot (1796-1832), the father of thermodynamics
Main article: History of thermodynamics
The history of thermodynamics as a scientific discipline generally begins with Otto von
Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated
a vacuum using hisMagdeburg hemispheres. Guericke was driven to make a vacuum in order to
disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke,
the Irish physicist and chemistRobert Boyle had learned of Guericke's designs and, in 1656, in
coordination with English scientistRobert Hooke, built an air pump.[10] Using this pump, Boyle
and Hooke noticed a correlation between pressure,temperature, and volume. In time, Boyle's
Law was formulated, which states that pressure and volume areinversely proportional. Then, in
1679, based on these concepts, an associate of Boyle's named Denis Papin built a bone
digester, which was a closed vessel with a tightly fitting lid that confined steam until a high
pressure was generated.
Later designs implemented a steam release valve that kept the machine from exploding. By
watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and
a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697,
based on Papin's designs, engineer Thomas Savery built the first engine. Although these early
engines were crude and inefficient, they attracted the attention of the leading scientists of the
time. Their work led 127 years later to Sadi Carnot, the "father of thermodynamics", who, in
1824, published Reflections on the Motive Power of Fire, a discourse on heat, power, and
engine efficiency. The paper outlined the basic energetic relations between the Carnot engine,
the Carnot cycle, and Motive power. It marked the start of thermodynamics as a modern
science.[3]. The termthermodynamics was coined by James Joule in 1849 to designate the
science of relations between heat andpower.[3] By 1858, "thermo-dynamics", as a functional
term, was used in William Thomson's paper An Account of Carnot's Theory of the Motive Power
of Heat.[11] The first thermodynamic textbook was written in 1859 by William Rankine, originally
trained as a physicist and a civil and mechanical engineering professor at the University of
Glasgow.[12]
Classical thermodynamics is the early 1800s variation of the original thermodynamics,
concerned with thermodynamic states and properties, such as energy, work and heat, and with
the laws of thermodynamics, all lacking an atomic interpretation.
In precursory form, classical thermodynamics derives from chemist Robert Boyle’s 1662
postulate that the pressure P of a given quantity of gas varies inversely as its volume V at
constant temperature; i.e. in equation form: PV = k, a constant. From here, a semblance of a
thermo-science began to develop with the construction of the first successful atmospheric steam
engines in England by Thomas Savery in 1697 andThomas Newcomen in 1712. The first and
second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the
works ofWilliam Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).
With the development of atomic and molecular theories in the late 1800s and early 1900s,
thermodynamics was given a molecular interpretation. This field, called statistical
mechanics or statistical thermodynamics, relates the microscopic properties of individual
atoms and molecules to the macroscopic or bulk properties of materials that can be observed in
everyday life, thereby explaining thermodynamics as a natural result of statistics and mechanics
(classical and quantum) at the microscopic level. The statistical approach is in contrast to
classical thermodynamics, which is a more phenomenological approach that does not include
microscopic details. The foundations of statistical thermodynamics were set out by physicists
such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard
Gibbs.
Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or
with a physical change of state within the confines of the laws of thermodynamics. During the
years 1873-76 the American mathematical physicist Josiah Willard Gibbs published a series of
three papers, the most famous being On the Equilibrium of Heterogeneous Substances, in
which he showed how thermodynamic processes could be graphically analyzed, by studying
the energy, entropy, volume, temperature and pressure of the thermodynamic system in such a
manner, one can determine if a process would occur spontaneously.[13] During the early 20th
century, chemists such as Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim began to
apply the mathematical methods of Gibbs to the analysis of chemical processes.[14]
[edit]The
Four Laws
Main article: Laws of thermodynamics
The present article is focused on classical thermodynamics, which is focused on systems
in thermodynamic equilibrium. It is wise to distinguish classical thermodynamics from nonequilibrium thermodynamics, which is concerned with systems that are not in thermodynamic
equilibrium.
In thermodynamics, there are four laws that do not depend on the details of the systems under
study or how they interact. Hence these laws are very generally valid, can be applied to systems
about which one knows nothing other than the balance of energy and matter transfer. Examples
of such systems include Einstein's prediction, around the turn of the 20th century,
of spontaneous emission, and ongoing research into the thermodynamics of black holes.
These four laws are:

Zeroth law of thermodynamics, about thermal equilibrium:
If two thermodynamic systems are separately in thermal equilibrium with a third, they are
also in thermal equilibrium with each other.
If we grant that all systems are (trivially) in thermal equilibrium with themselves, the
Zeroth law implies that thermal equilibrium is anequivalence relation on the set
of thermodynamic systems. This law is tacitly assumed in every measurement of
temperature. Thus, if we want to know if two bodies are at the same temperature, it is
not necessary to bring them into contact and to watch whether their observable
properties change with time.[15]
This law was considered so obvious it was added as a virtual after thought, hence the
designation Zeroth, rather than Fourth. In short, if the heat energy of material A is
equal to the heat energy of material B, and B is equal to the heat energy of material C.
then A and C must also be equal.

First law of thermodynamics, about the conservation of energy:
The change in the internal energy of a closed thermodynamic system is equal to the sum
of the amount of heat energy supplied to or removed from the system and the work done
on or by the system or we can say " In an isolated system the heat is constant".

Second law of thermodynamics, about entropy:
The total entropy of any isolated thermodynamic system always increases over time,
approaching a maximum value or we can say " in an isolated system, the entropy never
decreases". Another way to phrase this: Heat cannot spontaneously flow from a colder
location to a hotter area - work is required to achieve this.

Third law of thermodynamics, about the absolute zero of temperature:
As a system asymptotically approaches absolute zero of temperature all processes
virtually cease and the entropy of the system asymptotically approaches a minimum
value; also stated as: "the entropy of all systems and of all states of a system is zero at
absolute zero" or equivalently "it is impossible to reach the absolute zero of temperature
by any finite number of processes". Absolute zero, at which all activity would stop if it
were possible to happen, is −273.15 °C (degrees Celsius), or −459.67 °F (degrees
Fahrenheit) or 0 K (kelvins, formerly sometimes degrees absolute).
See also: Bose–Einstein condensate and negative temperature.
[edit]Potentials
Main article: Thermodynamic potentials
As can be derived from the energy balance equation (or Burks'
equation) on a thermodynamic system there exist energetic
quantities calledthermodynamic potentials, being the quantitative
measure of the stored energy in the system. The five most well
known potentials are:
Internal energy
Helmholtz free energy
Enthalpy
Gibbs free energy
Grand potential
Other thermodynamic potentials can be obtained
through Legendre transformation. Potentials are used to measure
energy changes in systems as they evolve from an initial state to a
final state. The potential used depends on the constraints of the
system, such as constant temperature or pressure. Internal
energy is the internal energy of the system, enthalpy is the internal
energy of the system plus the energy related to pressure-volume
work, and Helmholtz and Gibbs energy are the energies available
in a system to do useful work when the temperature and volume
or the pressure and temperature are fixed, respectively.
[edit]System
models
Main article: Thermodynamic system
An important concept in thermodynamics is the “system”.
Everything in the universe except the system is known as
surroundings. A system is the region of the universe under study.
A system is separated from the remainder of the universe by
a boundary which may be imaginary or not, but which by
convention delimits a finite volume. The possible exchanges
of work, heat, or matter between the system and the surroundings
take place across this boundary. Boundaries are of four types:
fixed, moveable, real, and imaginary.
Basically, the “boundary” is simply an imaginary dotted line drawn
around a volume of something when there is going to be a change
in the internal energy of that something. Anything that passes
across the boundary that effects a change in the internal energy of
the something needs to be accounted for in the energy balance
equation. That something can be the volumetric region
surrounding a single atom resonating energy, such as Max
Planck defined in 1900; it can be a body of steam or air in a steam
engine, such as Sadi Carnot defined in 1824; it can be the body of
a tropical cyclone, such as Kerry Emanuel theorized in 1986 in the
field of atmospheric thermodynamics; it could also be just
one nuclide (i.e. a system of quarks) as some are theorizing
presently in quantum thermodynamics.
For an engine, a fixed boundary means the piston is locked at its
position; as such, a constant volume process occurs. In that same
engine, a moveable boundary allows the piston to move in and
out. For closed systems, boundaries are real while for open
system boundaries are often imaginary. There are five dominant
classes of systems:
1. Isolated Systems – matter and energy may not cross the
boundary
2. Adiabatic Systems – heat must not cross the boundary
3. Diathermic Systems - heat may cross boundary
4. Closed Systems – matter may not cross the boundary
5. Open Systems – heat, work, and matter may cross the
boundary (often called a control volume in this case)
As time passes in an isolated system, internal differences in the
system tend to even out and pressures and temperatures tend to
equalize, as do density differences. A system in which all
equalizing processes have gone practically to completion, is
considered to be in a state ofthermodynamic equilibrium.
In thermodynamic equilibrium, a system's properties are, by
definition, unchanging in time. Systems in equilibrium are much
simpler and easier to understand than systems which are not in
equilibrium. Often, when analysing a thermodynamic process, it
can be assumed that each intermediate state in the process is at
equilibrium. This will also considerably simplify the situation.
Thermodynamic processes which develop so slowly as to allow
each intermediate step to be an equilibrium state are said to
be reversible processes.
[edit]Conjugate
variables
Main article: Conjugate variables (thermodynamics)
The central concept of thermodynamics is that of energy, the
ability to do work. By the First Law, the total energy of a system
and its surroundings is conserved. Energy may be transferred into
a system by heating, compression, or addition of matter, and
extracted from a system by cooling, expansion, or extraction of
matter. In mechanics, for example, energy transfer equals the
product of the force applied to a body and the resulting
displacement.
Conjugate variables are pairs of thermodynamic concepts, with
the first being akin to a "force" applied to some thermodynamic
system, the second being akin to the resulting "displacement," and
the product of the two equalling the amount of energy transferred.
The common conjugate variables are:

Pressure-volume (the mechanical parameters);

Temperature-entropy (thermal parameters);

Chemical potential-particle number (material parameters).
[edit]Instrumentation
Main article: Thermodynamic instruments
There are two types of thermodynamic instruments, the meter and
the reservoir. A thermodynamic meter is any device which
measures any parameter of a thermodynamic system. In some
cases, the thermodynamic parameter is actually defined in terms
of an idealized measuring instrument. For example, the zeroth
law states that if two bodies are in thermal equilibrium with a third
body, they are also in thermal equilibrium with each other. This
principle, as noted by James Maxwell in 1872, asserts that it is
possible to measure temperature. An idealizedthermometer is a
sample of an ideal gas at constant pressure. From the ideal gas
law pV=nRT, the volume of such a sample can be used as an
indicator of temperature; in this manner it defines temperature.
Although pressure is defined mechanically, a pressure-measuring
device, called a barometer may also be constructed from a
sample of an ideal gas held at a constant temperature.
A calorimeter is a device which is used to measure and define the
internal energy of a system.
A thermodynamic reservoir is a system which is so large that it
does not appreciably alter its state parameters when brought into
contact with the test system. It is used to impose a particular value
of a state parameter upon the system. For example, a pressure
reservoir is a system at a particular pressure, which imposes that
pressure upon any test system that it is mechanically connected
to. The Earth's atmosphere is often used as a pressure reservoir.
It is important that these two types of instruments are distinct. A
meter does not perform its task accurately if it behaves like a
reservoir of the state variable it is trying to measure. If, for
example, a thermometer were to act as a temperature reservoir it
would alter the temperature of the system being measured, and
the reading would be incorrect. Ideal meters have no effect on the
state variables of the system they are measuring.
[edit]States
& processes
Main article: Thermodynamic state
Main article: Thermodynamic processes
When a system is at equilibrium under a given set of conditions, it
is said to be in a definite state. The thermodynamic state of the
system can be described by a number of intensive
variables and extensive variables. The properties of the system
can be described by an equation of state which specifies the
relationship between these variables. State may be thought of as
the instantaneous quantitative description of a system with a set
number of variables held constant.
A thermodynamic process may be defined as the energetic
evolution of a thermodynamic system proceeding from an initial
state to a final state. Typically, each thermodynamic process is
distinguished from other processes, in energetic character,
according to what parameters, as temperature, pressure, or
volume, etc., are held fixed. Furthermore, it is useful to group
these processes into pairs, in which each variable held constant is
one member of a conjugate pair. The seven most common
thermodynamic processes are shown below:
1. An isobaric process occurs at constant pressure.
2. An isochoric process, or isometric/isovolumetric process,
occurs at constant volume.
3. An isothermal process occurs at a constant temperature.
4. An adiabatic process occurs without loss or gain of energy
by heat.
5. An isentropic process (reversible adiabatic process)
occurs at a constant entropy.
6. An isenthalpic process occurs at a constant enthalpy.
7. A steady state process occurs without a change in
the internal energy of a system.