Thermodynamics

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Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature on physical systems at the macroscopic scale. The starting point for most thermodynamic considerations are the laws of thermodynamics. These laws postulates that energy can be exchanged between physical systems in the form of heat and work, as well as the existence of a quantity named entropy, which can be associated with every system. In particular, the entropy of a system exchanging no heat with the outside can never decrease with time. As such, entropy allows predictions on the transformations and energy exchanges that are accessible to a given system.

Statistical mechanics is the underlying theory that sustains thermodynamics; it provides a way to predict the entropy of a thermodynamic system, based on the statistical analysis of the fluctuations that the system experiences over his set of microstates.

Overview

Thermodynamics can be divided into two main branches.

Equilibrium thermodynamics

Equilibrium thermodynamics studies systems as they approach equilibrium. This can be done by analyzing them from the macroscopic point of view, which is the classical approach. Alternatively, they can be analyzed from the microscopic perspective, which is the starting point of statistical thermodynamics.

While dealing with processes in which systems exchange matter or energy, classical thermodynamics is not concerned with the rate at which such processes take place, termed kinetics. For this reason, the term thermodynamics is usually used synonymously with equilibrium thermodynamics. A central notion for this connection is that of quasistatic processes, namely idealized, "infinitely slow" processes. Time-dependent thermodynamic processes are studied by non-equilibrium thermodynamics.

Non-equilibrium thermodynamics

Non-equilibrium thermodynamics studies the behavior of systems far away from equilibrium. This can be done through linear or non-linear analysis of irreversible processes, allowing systems near and far away from equilibrium to be studied, respectively.

Other branches of thermodynamics

From theoretical considerations and from interactions with other research fields, over the years, other variations of thermodynamics have come into their own, such as:

History

At its origins, thermodynamics was the study of engines. Prior to 1698 and the invention of the Savery Engine, horses were used to power pulleys, attached to buckets, which lifted water out of flooded salt mines in England. In the years to follow, more variations of steam engines were built, such as the Newcomen Engine, and later the Watt Engine. In time, these early engines would eventually be utilized in place of horses. Thus, each engine began to be associated with a certain amount of "horse power" depending upon how many horses it had replaced! The main problem with these first engines was that they were slow and clumsy, converting less than 2% of the input fuel into useful work. In other words, large quantities of coal (or wood) had to be burned to yield only a small fraction of work output. Hence the need for a new science of engine dynamics was born.

Most cite Sadi Carnot’s 1824 paper Reflections on the Motive Power of Fire as the starting point for thermodynamics as a modern science. Carnot defined "motive power" to be the expression of the useful effect that a motor is capable of producing. Herein, Carnot introduced us to the first modern day definition of "work": weight lifted through a height. The desire to understand, via formulation, this useful effect in relation to "work" is at the core of all modern day thermodynamics.

The name "thermodynamics", however, did not arrive until some twenty-five years later when in 1849, the British mathematician and physicist William Thomson (Lord Kelvin) coined the term ‘thermodynamics' in a paper on the efficiency of steam engines. In 1850, the famed mathematical physicist Rudolf Clausius originated and defined the term enthalpy H to be the total heat content of the system, stemming from the Greek word ‘enthalpein’ meaning to warm, and defined the term entropy S to be the heat lost or turned into waste, stemming from the Greek word ‘entrepein’ meaning to turn.

In association with Clausius, in 1871, a Scottish mathematician and physicist James Clerk Maxwell formulated a new branch of thermodynamics called Statistical Thermodynamics, which functions to analyze large numbers of particles at equilibrium, i.e. systems where no changes are occurring, such that only their average properties as temperature T, pressure P, and volume V become important.

Soon thereafter, in 1875, the Austrian physicist Ludwig Boltzmann formulated a precise connection between entropy S and molecular motion:

S=k\log W\,

being defined in terms of the number of possible states [W] such motion could occupy, where k is the Boltzmann's constant. The following year, 1876, was a seminal point in the development of human thought. During this essential period, chemical engineer Willard Gibbs, the first person in America to be awarded a PhD in engineering (Yale), published an obscure 300-pg paper titled: On the Equilibrium of Heterogeneous Substances, wherein he formulated one grand equality, the Gibbs free energy equation, which gives a measure the amount of "useful work" attainable in reacting systems.

Building on these foundations, those as Lars Onsager, Erwin Schrodinger, and Ilya Prigogine, and others, functioned to bring these engine “concepts” into the thoroughfare of almost every modern-day branch of science.

Thermodynamic parameters

The central concept of thermodynamics is that of energy, (measured in the SI-unit J). Energy may be transferred into a body either by compression or by heating, and extracted from a body either by expansion or by cooling. These processes make a heat engine.

So the most commonly considered thermodynamic parameters are:

Mechanical parameters:

Pressure: p (measured in Pa= J m^-3)
Volume: V (measured in m^-3 = J Pa^-1)

Thermal parameters:

Temperature: T (measured in K)
Entropy: S (measured in J K^-1)

The mechanical parameters can be described in terms of classical physics, while the thermal parameters are understood in terms of statistical mechanics.

A theoretical or experimental equations of state connect these parameters. The simplest and most important of these equations of state is the ideal gas law.

Thermodynamic potentials

Four quantities, called thermodynamic potentials, can be defined in terms of the thermodynamic parameters of a physical system:

Internal energy E: dE=TdS - pdV
Helmholtz free energy A: dA = −SdT - pdV
Gibbs free energy G: dG = −SdT + Vdp
Enthalpy H: dH = TdS + Vdp

Using the above differential forms of the four thermodynamic potentials, combined with the chain rule of product differentiation, the four potentials can be expressed in terms of each other and the thermodynamic parameters, as below:

$E=H-PV=A+TS$
$A=E-TS=G-PV$
$G=A+PV=H-TS$
$H=G+TS=E+PV$

The above relationships between the thermodynamic potentials and the thermodynamic parameters do not depend upon the particular system being studied; they are universal relationships that can be derived using statistical mechanics, with no regard for the forces or interaction potentials between the components of the system. However, the dependence of any one of these four thermodynamic potentials cannot be expressed in terms of the thermodynamic parameters of the system without knowledge of the interaction potentials between system components, the quantum energy levels and their corresponding degeneracies, or the partition function of the system under study. However, once the dependence of one of the thermodynamic functions upon the thermodynamic variables is determined, the three other thermodynamic potentials can be easily derived using the above equations.

Thermodynamic systems

A thermodynamic system is that part of the universe that is under consideration. A real or imaginary boundary separates the system from the rest of the universe, which is referred to as the environment or surroundings (sometimes called a reservoir.) A useful classification of thermodynamic systems is based on the nature of the boundary and the flows of matter, energy and entropy through it.

Interaction with surroundings

Three types of thermodynamic systems are disntinguished depending on the kinds of interaction and energy exchange taking place between the system and its surrounding environment:

Isolated systems: not exchanging heat, matter or work with their environment. Mathematically, this implies that TdS, dN, and pdV are all zero, and therefore dE is zero. An example of an isolated system would be an insulated container, such as an insulated gas cylinder.
Closed systems: exchanging energy (heat and work) but not matter with their environment. In this case, only dN is generally zero. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary, which can be
- adiabatic boundary: not allowing heat exchange, TdS = 0
- rigid boundary: not allowing exchange of work, pdV = 0
open systems: exchanging energy (heat and work) and matter with their environment. A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system.

In reality, a system can never be absolutely isolated from its environment, because there is always at least some slight coupling, even if only via minimal gravitational attraction. In analyzing a system in steady-state, the energy into the system is equal to the energy leaving the system. _[1]

When a system is at equilibrium under a given set of conditions, it is said to be in a definite state. The 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.

Thermodynamic states

Every thermodynamic system can be described by a set of thermodynamic parameters; an optimal ensemble of parameters that uniquely specify the macroscopic condition of the system is said to be its state, from these all other parameters can be derived. Depending on the characteristic of a system, a varying number of parameters are needed to describe its state.

Blackbody radiation is an example of a state that is completely described by temperature, although if phase transitions or spontaneous symmetry breaking occur other variables may be needed to discriminate among the phases. (This problem does not arise for blackbody radiation.) Given the internal energy as a function of temperature, we can define A = U - TS.
Most "pure" nonmagnetic substances fall into this category. Their states are completely described by temperature and pressure, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase. Given U and V (or the density ρ) as a function of T and P, we can define the Helmholtz energy as before and the Gibbs energy as G = U - TS + PV and the enthalpy as H = U + PV.
If there are more than one kind of atom/molecule in a system, its state must be described by temperature, pressure, and chemical potentials, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.
If a substance is a ferromagnet or a superconductor, its state is described by temperature and a magnetic field, except at phase transitions and perhaps spontaneous symmetry breaking in the ordered phase.

The laws of thermodynamics

In thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. This means they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer. Examples of this include Einstein's prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes. Alternative statements that are mathematically equivalent can be given for each law.

The four laws are:

Zeroth law of thermodynamics, about the transitivity of thermodynamic equilibrium
- If A and B are in thermal equilibrium, and B and C are in thermal equilibrium, then A and C are also in thermal equilibrium.
- Two systems in thermal equilibrium with a third system, all must be in equilibrium with each other.
First law of thermodynamics, or a statement about the conservation of energy
- The work exchanged in an adiabatic process depends only on the initial and the final state and not on the details of the process.
- The heat energy flowing into a system is equal to the sum of the increase in the internal energy of the system and the work done by the system.
Second law of thermodynamics, about entropy
- It is impossible to obtain a process such that the unique effect is the subtraction of a positive heat from a reservoir and the production of a positive work.
- The entropy of a closed system never decreases (see Maxwell's demon)
- A system operating in contact with a thermal reservoir cannot produce positive work in its surroundings (Kelvin)
- A system operating in a cycle cannot produce a positive heat flow from a colder body to a hotter body (Clausius)
Third law of thermodynamics, about absolute zero temperature
- All processes cease as temperature approaches zero.
- As temperature goes to 0, the entropy of a system approaches a constant

The laws of thermodynamics and mechanics

The second Law of thermodynamics is an exact consequence of the laws of mechanics—classical or quantum. The Fluctuation Theorem shows that the Second Law of Thermodynamics is also an exact consequence of the laws of mechanics except that it is only valid in the large system or long time limit.

Quotes & humor

"Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." — Albert Einstein
"In this house, we obey the laws of thermodynamics!" (after Lisa constructs a perpetual motion machine whose energy increases with time) — Homer Simpson
"The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." — Sir Arthur Eddington

“There’s as many variations of the second law of thermodynamics as there are thermodynamicists.”
A common scientific joke expresses the three laws simply (and surprisingly accurately) as:

Zeroth: You must play the game

First: You can't win.

Second: You can't break even.

Third: You can't quit the game.

References

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