Thermodynamics

Thermodynamics is a branch of physics that examines the interrelationships among heat, work, and temperature, and their connection to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which provide a quantitative description using measurable macroscopic physical quantities, yet can be elucidated in terms of microscopic constituents through statistical mechanics. Thermodynamics finds application across diverse scientific and engineering disciplines, notably physical chemistry, biochemistry, chemical engineering, and mechanical engineering, alongside complex fields such as meteorology.

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology.

Historically, thermodynamics originated from the impetus to enhance the efficiency of early steam engines, a development significantly influenced by the work of French physicist Sadi Carnot (1824). Scots-Irish physicist Lord Kelvin first articulated a concise definition of thermodynamics in 1854, stating, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." German physicist and mathematician Rudolf Clausius rearticulated Carnot's principle, known as the Carnot cycle, thereby establishing a more accurate and rigorous foundation for the theory of heat. His seminal paper, "On the Moving Force of Heat," published in 1850, first enunciated the second law of thermodynamics. In 1865, he coined the term entropy, and in 1870, he introduced the virial theorem, which he applied to thermal phenomena.

The initial application of thermodynamics to mechanical heat engines rapidly expanded to encompass the study of chemical compounds and reactions. Chemical thermodynamics investigates the role of entropy in chemical reaction processes and has significantly advanced the field's understanding and scope. Concurrently, other formulations of thermodynamics emerged. Statistical thermodynamics, also known as statistical mechanics, focuses on statistical predictions concerning the collective motion of particles based on their microscopic behavior. In 1909, Constantin Carathéodory presented a purely mathematical approach within an axiomatic framework, a description frequently termed geometrical thermodynamics.

Introduction

The description of any thermodynamic system is predicated upon the four laws of thermodynamics, which constitute its axiomatic foundation. The first law postulates that energy can be transferred between physical systems as heat, as work, and through the transfer of matter. The second law defines the existence of a quantity called entropy, which dictates the thermodynamic direction of system evolution, quantifies the system's state of order, and enables the determination of extractable useful work.

Within thermodynamics, interactions among macroscopic aggregates of entities are systematically studied and categorized. Central to this framework are the concepts of the thermodynamic system and its surroundings. A system comprises particles whose collective average motions determine its properties, and these properties are interlinked through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are instrumental in establishing criteria for equilibrium and spontaneous processes.

Leveraging these principles, thermodynamics enables the description of how systems respond to changes in their environment. This finds application across a wide variety of topics in science and engineering, including engines, phase transitions, chemical reactions, transport phenomena, and even black holes. Thermodynamic principles are fundamental to other fields of physics and to chemistry, chemical engineering, corrosion engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, materials science, and economics.

This article primarily addresses classical thermodynamics, which investigates systems predominantly in thermodynamic equilibrium. Non-equilibrium thermodynamics is frequently considered an extension of the classical treatment, though statistical mechanics has significantly advanced that field.

History

The scientific discipline of thermodynamics traces its origins to Otto von Guericke, who in 1650, constructed the inaugural vacuum pump and showcased a vacuum using his Magdeburg hemispheres. Guericke's motivation was to refute Aristotle's enduring hypothesis that 'nature abhors a vacuum'. Subsequently, in 1656, the Anglo-Irish physicist and chemist Robert Boyle, collaborating with English scientist Robert Hooke, developed an air pump, drawing inspiration from Guericke's innovations. Through experiments with this pump, Boyle and Hooke observed a relationship among pressure, temperature, and volume. This led to the formulation of Boyle's Law, which posits an inverse proportionality between pressure and volume. Building upon these foundational principles in 1679, Denis Papin, an associate of Boyle, engineered a steam digester—a sealed vessel designed to contain steam until significant pressure accumulated.

Subsequent iterations incorporated a steam release valve, preventing catastrophic explosions. Observing the rhythmic motion of this valve, Papin conceptualized the piston and cylinder engine; however, he did not advance this design to fruition. Nonetheless, in 1697, Thomas Savery constructed the first engine, drawing upon Papin's concepts, with Thomas Newcomen following suit in 1712. Despite their rudimentary and inefficient nature, these nascent engines garnered considerable interest from prominent contemporary scientists.

Professor Joseph Black at the University of Glasgow, where James Watt worked as an instrument maker, developed the foundational concepts of heat capacity and latent heat, which were crucial for the advancement of thermodynamics. Black and Watt collaborated on experiments, but Watt originated the concept of the external condenser, significantly enhancing steam engine efficiency. Synthesizing these prior contributions, Sadi Carnot, recognized as the "father of thermodynamics," published Reflections on the Motive Power of Fire (1824). This seminal work explored heat, power, energy, and engine efficiency, delineating the fundamental energetic relationships among the Carnot engine, the Carnot cycle, and motive power, thereby inaugurating thermodynamics as a modern scientific discipline.

William Rankine, a physicist by training and a professor of civil and mechanical engineering at the University of Glasgow, authored the inaugural textbook on thermodynamics in 1859. Concurrently, during the 1850s, the first and second laws of thermodynamics were established, largely through the contributions of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin). Subsequently, physicists including James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius, and J. Willard Gibbs laid the groundwork for statistical thermodynamics.

Rudolf Clausius, often cited as "one of the founding fathers of thermodynamics," first articulated the fundamental principles of the second law in his 1850 paper, "On the Moving Force of Heat," and subsequently introduced the concept of entropy in 1865.

Between 1873 and 1876, the American mathematical physicist Josiah Willard Gibbs published a series of three influential papers, notably On the Equilibrium of Heterogeneous Substances. In this work, Gibbs demonstrated a graphical method for analyzing thermodynamic processes, including chemical reactions, by examining the energy, entropy, volume, temperature, and pressure of a thermodynamic system to ascertain the spontaneity of a process. Concurrently, Pierre Duhem also contributed to the field of chemical thermodynamics in the 19th century. In the early 20th century, chemists including Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim further applied Gibbs' mathematical methodologies to the analysis of chemical processes.

Etymology

The term Thermodynamics possesses a complex etymology.

A superficial etymological examination reveals that the word comprises two components originating from Ancient Greek. The prefix thermo- ("of heat," as seen in terms like thermometer) derives from the root θέρμη therme, signifying "heat." The second component, dynamics ("science of force or power"), stems from the root δύναμις dynamis, meaning "power."

William Thomson employed the adjective thermo-dynamic in 1849.

By 1854, Thomson and William Rankine utilized the noun thermo-dynamics to denote the scientific study of generalized heat engines.

Pierre Perrot asserts that the term thermodynamics was coined by James Joule in 1858 to describe the scientific study of the relationship between heat and power; however, Joule himself never employed this specific term, instead utilizing the phrase perfect thermo-dynamic engine in reference to Thomson's 1849 phraseology.

Subdisciplines of Thermodynamics

The investigation of thermodynamic systems has diversified into numerous interconnected branches, each employing a distinct fundamental model as its theoretical or empirical foundation, or applying thermodynamic principles to diverse system classifications.

Classical Thermodynamics

Classical thermodynamics characterizes the states of thermodynamic systems operating near equilibrium, employing macroscopic and quantifiable properties. This branch models the transfers of energy, work, and heat, grounded in the fundamental laws of thermodynamics. The designation classical signifies its foundational role as the initial conceptual framework for the subject, emerging in the 19th century, and its description of system transformations using macroscopic, empirically observable parameters. A subsequent microscopic interpretation of these principles was furnished through the evolution of statistical mechanics.

Statistical Mechanics

Statistical mechanics, also known as statistical thermodynamics, arose concurrently with the advancement of atomic and molecular theories during the late 19th and early 20th centuries, and augmented classical thermodynamics by providing an interpretation of microscopic interactions among individual particles or quantum-mechanical states. This discipline establishes connections between the microscopic characteristics of individual atoms and molecules and the macroscopic, bulk properties of materials perceptible at the human scale, thereby elucidating classical thermodynamics as an emergent consequence of statistical principles, classical mechanics, and quantum theory at the microscopic scale.

Chemical Thermodynamics

Chemical thermodynamics investigates the energetic interrelationships associated with chemical reactions or physical phase transitions, operating within the framework of thermodynamic laws. A principal aim of chemical thermodynamics involves ascertaining the spontaneity of a particular transformation.

Equilibrium Thermodynamics

Equilibrium thermodynamics focuses on the transfers of matter and energy within systems or entities that can be transitioned from one state of thermodynamic equilibrium to another through external environmental influences. The concept of 'thermodynamic equilibrium' denotes a balanced condition where all macroscopic fluxes are absent; for elementary systems or bodies, this implies homogeneous intensive properties and pressures exerted perpendicularly to their boundaries. Within an equilibrium state, no unbalanced potentials or driving forces exist between macroscopically discernible components of the system. A primary objective in equilibrium thermodynamics is to determine the final equilibrium state of a system, subsequent to a defined thermodynamic operation altering its boundaries or environment, given its initial well-defined equilibrium state, its surroundings, and its constitutive walls.

Non-Equilibrium Thermodynamics

Non-equilibrium thermodynamics constitutes a subfield of thermodynamics concerned with systems that have not attained thermodynamic equilibrium. The majority of naturally occurring systems do not exist in thermodynamic equilibrium, as they are not in stationary states and are perpetually or intermittently exposed to fluxes of matter and energy exchanged with other systems. The thermodynamic analysis of non-equilibrium systems necessitates the application of more generalized concepts than those employed in equilibrium thermodynamics. Numerous natural systems presently continue to lie outside the purview of established macroscopic thermodynamic methodologies.

Laws of Thermodynamics

Thermodynamics is fundamentally predicated upon a quartet of laws, each possessing universal validity when applied to systems conforming to their inherent constraints. While these laws may be articulated in ostensibly distinct forms across various theoretical frameworks of thermodynamics, the most widely recognized formulations are presented below.

Zeroth Law

The Zeroth Law of Thermodynamics postulates that: If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

This principle establishes thermal equilibrium as an equivalence relation within the defined set of thermodynamic systems. Systems achieve equilibrium when minor, stochastic interactions, such as Brownian motion, result in no net energy transfer. This law is implicitly fundamental to all temperature measurements. Consequently, determining if two bodies possess identical temperatures does not necessitate their direct contact or the observation of temporal changes in their properties. The law thus offers an empirical definition of temperature and validates the development of functional thermometers.

Initially, the zeroth law was not formally recognized as a distinct thermodynamic principle, primarily because its foundation in thermodynamic equilibrium was already inherent in the other established laws. The first, second, and third laws had already been explicitly articulated and widely accepted within the physics community before the critical role of the zeroth law in defining temperature was fully appreciated. Given the impracticality of renumbering the existing laws, it was subsequently designated as the zeroth law.

First Law

The first law of thermodynamics posits that, for a process involving no matter transfer, the alteration in a thermodynamic system's internal energy, denoted as ${\displaystyle \Delta U}$, is equivalent to the thermal energy acquired, represented by ${\displaystyle Q}$, minus the thermodynamic work, symbolized as ${\displaystyle W}$, performed by the system on its environment.

${\displaystyle \Delta U=Q-W}$.

Here, ${\displaystyle \Delta U}$ signifies the alteration in the internal energy of a closed system, where energy exchange via heat or work across the system boundary is permissible, but matter transfer is prohibited. ${\displaystyle Q}$ represents the thermal energy transferred to the system, and ${\displaystyle W}$ indicates the thermodynamic work performed by the system on its environment. An alternative formulation asserts the impossibility of perpetual motion machines of the first kind; specifically, any work ${\displaystyle W}$ executed by a system on its surroundings necessitates a reduction or consumption of the system's internal energy ${\displaystyle U}$. Consequently, the internal energy expended for such work must be replenished as heat ${\displaystyle Q}$ from an external energy source or as work performed by an external mechanism acting upon the system (thereby restoring ${\displaystyle U}$) to enable continuous operation.

For processes involving matter transfer, an additional postulate is required: Considering the respective fiducial reference states of the systems, if two systems, potentially differing in chemical composition, are initially segregated solely by an impermeable barrier and are otherwise isolated, their combination into a new system through the thermodynamic removal of this barrier implies that

U §1011§ = U §2021§ + U §3031§ {\displaystyle U_{0}=U_{1}+U_{2}} ,

where U§56§ represents the internal energy of the composite system, while U§1314§ and U§2122§ signify the internal energies of the individual, separated systems.

When applied to thermodynamics, this law articulates the principle of energy conservation, asserting that energy can undergo transformation into different forms but cannot be generated or annihilated.

Internal energy constitutes a fundamental characteristic of a thermodynamic state, whereas heat and work represent mechanisms of energy transfer that can alter this state. Modifications to a system's internal energy can result from any combination of heat exchange (addition or removal) and work executed on or by the system. As a state function, internal energy is independent of the specific process or the sequence of intermediate stages through which the system reaches its current state.

Second Law

A classical formulation of the second law of thermodynamics posits that: Heat does not spontaneously flow from a colder body to a hotter body.

The second law pertains to a system comprising matter and radiation, initially characterized by heterogeneities in temperature, pressure, chemical potential, and other intensive properties. These inhomogeneities arise from internal constraints, such as impermeable rigid walls, or from externally applied forces. The law stipulates that when such a system is isolated from its external environment and from these forces, a specific thermodynamic quantity, its entropy, will increase as these constraints are progressively removed. This increase continues until entropy reaches a maximum value at thermodynamic equilibrium, at which point the inhomogeneities effectively disappear. For systems initially distant from thermodynamic equilibrium, despite various proposals, no universal physical principle is known to dictate the rates at which they approach equilibrium; thermodynamics itself does not address these rates. The numerous interpretations of the second law consistently underscore the inherent irreversibility of the transitions observed as systems evolve towards thermodynamic equilibrium.

Within macroscopic thermodynamics, the second law functions as a fundamental observation pertinent to any real thermodynamic process. Conversely, in statistical thermodynamics, this law is theorized to emerge as a direct consequence of molecular chaos.

Third Law

The third law of thermodynamics asserts that: As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.

This thermodynamic law represents a statistical principle of nature concerning entropy and the inherent impossibility of attaining absolute zero temperature. It establishes an absolute reference point for entropy determination, from which the absolute entropy is derived. Alternative formulations include the statement that "the entropy of all systems and of all states of a system is smallest at absolute zero," or, equivalently, that "it is impossible to reach the absolute zero of temperature by any finite number of processes."

Absolute zero, the theoretical temperature at which all molecular activity would cease if attainable, corresponds to −273.15 °C (degrees Celsius), −459.67 °F (degrees Fahrenheit), 0 K (kelvin), or 0° R (degrees Rankine).

System Models

A pivotal concept in thermodynamics is the thermodynamic system, defined as a precisely delineated region of the universe under investigation. All entities within the universe external to this system are collectively termed the surroundings. A system is demarcated from the rest of the universe by a boundary, which can be either physical or conceptual, but invariably serves to enclose the system within a finite volume. Portions of this boundary are frequently referred to as walls, each possessing specific, defined permeabilities. The exchange of energy, whether as work or heat, or the transfer of matter between the system and its surroundings, occurs across these walls, contingent upon their respective permeabilities.

Any matter or energy traversing the system boundary and altering its internal energy must be included in the energy balance equation. The volume enclosed by these boundaries can range from the region around a single energy-resonating atom, as defined by Max Planck in 1900, to a mass of steam or air within a steam engine, as conceptualized by Sadi Carnot in 1824. In quantum thermodynamics, a system might even consist of a single nuclide (i.e., a quark system). Adopting a broader perspective that relaxes the thermodynamic equilibrium requirement allows the system to encompass entities like a tropical cyclone, as theorized by Kerry Emanuel in 1986 within atmospheric thermodynamics, or the event horizon of a black hole.

Boundaries are categorized into four types: fixed, movable, real, and imaginary. For instance, in an engine, a fixed boundary implies the piston is stationary, potentially facilitating a constant volume process. Conversely, if the piston is permitted to move, that boundary becomes movable, while the cylinder and cylinder head boundaries remain fixed. Closed systems typically feature real boundaries, whereas open systems often utilize imaginary boundaries. Consider a jet engine: a fixed imaginary boundary might be posited at the engine's intake, with fixed real boundaries along the casing surface, and another fixed imaginary boundary across the exhaust nozzle.

Thermodynamics generally classifies systems into three categories, based on the permissible transfer of matter and energy across their boundaries:

Within an isolated system, internal disparities in pressure, density, and temperature progressively diminish over time. A system where all such equalization processes have concluded is defined as being in a state of thermodynamic equilibrium.

By definition, a system's properties remain constant once thermodynamic equilibrium is attained. Equilibrium systems are considerably less complex and more readily comprehensible than non-equilibrium systems. During the analysis of dynamic thermodynamic processes, a common simplifying assumption is that each intermediate state exists in equilibrium. This leads to the concept of reversible processes, which evolve sufficiently slowly to ensure that every intermediate step constitutes an equilibrium state.

States and Processes

A system operating under a specific set of conditions and in equilibrium is considered to be in a definite thermodynamic state. This state is characterized by various state quantities, which are independent of the pathway taken to reach that state. These quantities are classified as either intensive or extensive variables, depending on their behavior with changes in system size. The system's properties are further elucidated by an equation of state, which defines the relationships among these variables. Conceptually, a state represents an instantaneous quantitative description of a system where a specific number of variables are maintained constant.

A thermodynamic process is defined as the energetic transformation of a thermodynamic system from an initial to a final state, quantifiable through process quantities. Each thermodynamic process is typically differentiated by its energetic characteristics, specifically by which parameters (e.g., temperature, pressure, or volume) are held constant. Moreover, it is often advantageous to categorize these processes into pairs, where each constant variable corresponds to one member of a conjugate pair.

Several frequently studied thermodynamic processes include:

• Adiabatic process: A process occurring without any transfer of energy as heat.
• Isenthalpic process: A process characterized by constant enthalpy.
• Isentropic process: A reversible adiabatic process, occurring at constant entropy.
• Isobaric process: A process maintained at constant pressure.
• Isochoric process: A process occurring at constant volume, also known as isometric or isovolumetric.
• Isothermal process: A process conducted at a constant temperature.
• Steady-state process: A process characterized by no change in internal energy over time.

Instrumentation

Thermodynamic instrumentation is categorized into two primary types: meters and reservoirs. A thermodynamic meter functions as any apparatus designed to quantify a parameter within a thermodynamic system. In certain instances, a thermodynamic parameter is conceptually defined by an idealized measuring instrument. For example, the zeroth law of thermodynamics posits that if two distinct bodies are in thermal equilibrium with a third body, they are consequently in thermal equilibrium with each other. This principle, as articulated by James Maxwell in 1872, establishes the feasibility of temperature measurement. An idealized thermometer, for instance, consists of an ideal gas sample maintained at constant pressure. According to the ideal gas law, pV=nRT, the volume of such a sample can serve as a direct indicator of temperature, thereby defining it. While pressure is fundamentally defined mechanically, a device for measuring pressure, known as a barometer, can similarly be constructed from an ideal gas sample kept at a constant temperature. A calorimeter is an instrument specifically employed to measure and define a system's internal energy.

A thermodynamic reservoir is characterized as a system of such substantial magnitude that its state parameters remain negligibly altered when it interacts with a system of interest. Upon contact between the reservoir and the system, the latter achieves equilibrium with the former. For instance, a pressure reservoir is a system maintained at a specific pressure, which then imposes that pressure upon any system to which it is mechanically connected. The Earth's atmosphere frequently serves as a pressure reservoir. Similarly, the ocean can function as a temperature reservoir, particularly when utilized for cooling power plants.

Conjugate Variables

The fundamental concept in thermodynamics is energy, defined as the capacity to perform work. In accordance with the First Law of Thermodynamics, the total energy of a system and its surroundings is conserved. Energy can be introduced into a system through processes such as heating, compression, or the addition of matter, and can be extracted via cooling, expansion, or the removal of matter. In mechanical contexts, for example, energy transfer is equivalent to the product of an applied force on a body and the resulting displacement.

Conjugate variables represent pairs of thermodynamic quantities where the first variable is analogous to a "force" exerted on a thermodynamic system, and the second is analogous to the resultant "displacement." The product of these two variables quantifies the amount of energy transferred. The commonly recognized conjugate variable pairs include:

• Pressure–volume (representing mechanical parameters);
• Temperature–entropy (representing thermal parameters);
• Chemical potential–particle number (representing material parameters).

Potentials

Thermodynamic potentials are distinct quantitative metrics that characterize the stored energy within a system. These potentials are utilized to quantify energy transformations in systems as they transition from an initial to a final state. The specific potential employed is contingent upon the system's constraints, such as constant temperature or pressure. For example, the Helmholtz and Gibbs energies represent the available energy within a system for useful work when temperature and volume, or pressure and temperature, are held constant, respectively. While thermodynamic potentials are not directly measurable in laboratory settings, they can be computed using molecular thermodynamics.

The five most prominent potentials are:

where ${\displaystyle T}$ denotes temperature, ${\displaystyle S}$ represents entropy, ${\displaystyle p}$ signifies pressure, ${\displaystyle V}$ indicates volume, ${\displaystyle \mu }$ is the chemical potential, ${\displaystyle N}$ denotes the number of particles within the system, and ${\displaystyle i}$ represents the count of distinct particle types in the system.

Thermodynamic potentials are derivable from the energy balance equation when applied to a thermodynamic system. Additionally, other thermodynamic potentials can be generated via Legendre transformation.

Axiomatic Thermodynamics

Axiomatic thermodynamics constitutes a mathematical discipline focused on articulating thermodynamics through rigorous axioms, such as establishing a mathematically precise formulation for the established laws of thermodynamics.

The initial endeavor to establish an axiomatic theory of thermodynamics was Constantin Carathéodory's 1909 publication, Investigations on the Foundations of Thermodynamics. This work employed Pfaffian systems and introduced the concept of adiabatic accessibility. Within this framework, fundamental thermodynamic concepts like heat, entropy, and temperature are deduced from more directly quantifiable measurements. Subsequent theories diverged by positing assumptions about thermodynamic processes involving arbitrary initial and final states, rather than exclusively examining proximate states.

Applied Fields

Thermodynamic Process Path

• Thermodynamic process path

List of Significant Publications in Thermodynamics

• List of important publications in thermodynamics
• List of Textbooks on Thermodynamics and Statistical Mechanics
• List of Thermal Conductivities
• List of Thermodynamic Properties
• Table of Thermodynamic Equations
• Timeline of Thermodynamics
• Thermodynamic Equations

References

Goldstein, Martin & Inge F. (1993). The Refrigerator and the Universe. Harvard University Press. ISBN 978-0-674-75325-9. OCLC 32826343. This work offers a non-technical introduction, notable for its historical and interpretive insights.

• Goldstein, Martin & Inge F. (1993). The Refrigerator and the Universe. Harvard University Press. ISBN 978-0-674-75325-9. OCLC 32826343.Kazakov, Andrei; Muzny, Chris D.; Chirico, Robert D.; Diky, Vladimir V.; Frenkel, Michael (2008). "Web Thermo Tables – an On-Line Version of the TRC Thermodynamic Tables". Journal of Research of the National Institute of Standards and Technology. 113 (4): 209–220. doi:10.6028/jres.113.016. ISSN 1044-677X. PMC 4651616. PMID 27096122.Gibbs J.W. (1928). The Collected Works of J. Willard Gibbs Thermodynamics. New York: Longmans, Green and Co.Guggenheim E.A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs. London: Methuen & Co. Ltd.Denbigh K. (1981). The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering. London: Cambridge University Press.Stull, D.R., Westrum Jr., E.F. and Sinke, G.C. (1969). The Chemical Thermodynamics of Organic Compounds. London: John Wiley and Sons, Inc.
• Bazarov I.P. (2010). Thermodynamics: Textbook. St. Petersburg: Lan Publishing House. Page 384. ISBN 978-5-8114-1003-3.Bawendi Moungi G., Alberty Robert A. and Silbey Robert J. (2004). Physical Chemistry. J. Wiley & Sons, Incorporated.Alberty Robert A. (2003). Thermodynamics of Biochemical Reactions. Wiley-Interscience.Alberty Robert A. (2006). Biochemical Thermodynamics: Applications of Mathematica. Volume 48. John Wiley & Sons, Inc. Pages 1–458. ISBN 978-0-471-75798-6. PMID 16878778.:
• Dill Ken A., Bromberg Sarina (2011). Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience. Garland Science. ISBN 978-0-8153-4430-8.M. Scott Shell (2015). Thermodynamics and Statistical Mechanics: An Integrated Approach. Cambridge University Press. ISBN 978-1107656789.Douglas E. Barrick (2018). Biomolecular Thermodynamics: From Theory to Applications. CRC Press. ISBN 978-1-4398-0019-5.Bejan, Adrian (2016). Advanced Engineering Thermodynamics (4th ed.). Wiley. ISBN 978-1-119-05209-8.Cengel, Yunus A., and Boles, Michael A. (2002). Thermodynamics – an Engineering Approach. McGraw Hill. ISBN 978-0-07-238332-4. OCLC 45791449.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Dunning-Davies, Jeremy (1997). Concise Thermodynamics: Principles and Applications. Horwood Publishing. ISBN 978-1-8985-6315-0. OCLC 36025958.Kroemer, Herbert, and Kittel, Charles (1980). Thermal Physics. W.H. Freeman Company. ISBN 978-0-7167-1088-2. OCLC 32932988.
  • Media related to Thermodynamics at Wikimedia Commons
  • Callendar, Hugh Longbourne (1911). "Thermodynamics". In Encyclopædia Britannica. Vol. 26 (11th ed.). pp. 808–814.Source: TORIma Academy Archive