Thermodynamics |
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**Enthalpy** /ˈɛnθəlpi/ ( listen ), a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume.^{ [1] } It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings.^{ [2] }^{ [3] } The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.

- Definition
- Other expressions
- Characteristic functions and natural state variables
- Physical interpretation
- Relationship to heat
- Applications
- Heat of reaction
- Specific enthalpy
- Enthalpy changes
- Open systems
- Diagrams
- Some basic applications
- Throttling
- Compressors
- History and etymology
- See also
- Notes
- References
- Bibliography
- External links

In the International System of Units (SI), the unit of measurement for enthalpy is the joule. Other historical conventional units still in use include the calorie and the British thermal unit (BTU).

The total enthalpy of a system cannot be measured directly because the internal energy contains components that are unknown, not easily accessible, or are not of interest in thermodynamics. In practice, a change in enthalpy is the preferred expression for measurements at constant pressure because it simplifies the description of energy transfer. When transfer of matter into or out of the system is also prevented and no electrical or shaft work is done, at constant pressure the enthalpy change equals the energy exchanged with the environment by heat.

In chemistry, the standard enthalpy of reaction is the enthalpy change when reactants in their standard states (*p* = 1 bar; usually *T* = 298 K) change to products in their standard states.^{ [4] } This quantity is the standard heat of reaction at constant pressure and temperature, but it can be measured by calorimetric methods even if the temperature does vary during the measurement, provided that the initial and final pressure and temperature correspond to the standard state. The value does not depend on the path from initial to final state because enthalpy is a state function.

Enthalpies of chemical substances are usually listed for 1 bar (100 kPa) pressure as a standard state. Enthalpies and enthalpy changes for reactions vary as a function of temperature,^{ [5] } but tables generally list the standard heats of formation of substances at 25 °C (298 K). For endothermic (heat-absorbing) processes, the change Δ*H* is a positive value; for exothermic (heat-releasing) processes it is negative.

The enthalpy of an ideal gas is independent of its pressure or volume, and depends only on its temperature, which correlates to its thermal energy. Real gases at common temperatures and pressures often closely approximate this behavior, which simplifies practical thermodynamic design and analysis.

The enthalpy *H* of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume:^{ [1] }

*H*=*U*+*pV*,

where *U* is the internal energy, p is pressure, and V is the volume of the system; pV is sometimes referred to as the pressure energy ƐP.^{[ citation needed ]}

Enthalpy is an extensive property; it is proportional to the size of the system (for homogeneous systems). As intensive properties, the specific enthalpy *h* = *H*/*m* is referenced to a unit of mass m of the system, and the molar enthalpy *H*_{m} is *H*/*n*, where n is the number of moles. For inhomogeneous systems the enthalpy is the sum of the enthalpies of the component subsystems:

where

- H is the total enthalpy of all the subsystems,
- k refers to the various subsystems,
- H
_{k}refers to the enthalpy of each subsystem.

A closed system may lie in thermodynamic equilibrium in a static gravitational field, so that its pressure p varies continuously with altitude, while, because of the equilibrium requirement, its temperature T is invariant with altitude. (Correspondingly, the system's gravitational potential energy density also varies with altitude.) Then the enthalpy summation becomes an integral:

where

- ρ ("rho") is density (mass per unit volume),
- h is the specific enthalpy (enthalpy per unit mass),
- (
*ρh*) represents the enthalpy density (enthalpy per unit volume), - dV denotes an infinitesimally small element of volume within the system, for example, the volume of an infinitesimally thin horizontal layer,the integral therefore represents the sum of the enthalpies of all the elements of the volume.

The enthalpy of a closed homogeneous system is its energy function *H*(*S*,*p*), with its entropy *S*[*p*] and its pressure p as natural state variables which provide a differential relation for of the simplest form, derived as follows. We start from the first law of thermodynamics for closed systems for an infinitesimal process:

where

- 𝛿
*Q*is a small amount of heat added to the system, - 𝛿
*W*is a small amount of work performed by the system.

In a homogeneous system in which only reversible processes or pure heat transfer are considered, the second law of thermodynamics gives 𝛿*Q* = *T**dS*, with T the absolute temperature and dS the infinitesimal change in entropy S of the system. Furthermore, if only pV work is done, 𝛿*W* = *p**dV*. As a result,

Adding *d*(*pV*) to both sides of this expression gives

or

So

and the coefficients of the natural variable differentials and are just the single variables and .

The above expression of dH in terms of entropy and pressure may be unfamiliar to some readers. There are also expressions in terms of more directly measurable variables such as temperature and pressure:^{ [6] }^{: 88 }^{ [7] }

Here *C*_{p} is the heat capacity at constant pressure and α is the coefficient of (cubic) thermal expansion:

With this expression one can, in principle, determine the enthalpy if C_{p} and V are known as functions of p and T. However the expression is more complicated than because T is not a natural variable for the enthalpy H.

At constant pressure, so that For an ideal gas, reduces to this form even if the process involves a pressure change, because *αT* = 1,^{ [note 1] }.

In a more general form, the first law describes the internal energy with additional terms involving the chemical potential and the number of particles of various types. The differential statement for dH then becomes

where *μ*_{i} is the chemical potential per particle for an i-type particle, and *N*_{i} is the number of such particles. The last term can also be written as *μ _{i}*

The enthalpy, *H*(*S*[*p*], *p*, {*N _{i}*}), expresses the thermodynamics of a system in the

Conjugate with the enthalpy, with these arguments, the other characteristic function of state of a thermodynamic system is its entropy, as a function, *S*[*p*](*H*, *p*, {*N _{i}*}), of the same list of variables of state, except that the entropy,

The U term is the energy of the system, and the pV term can be interpreted as the work that would be required to "make room" for the system if the pressure of the environment remained constant. When a system, for example, n moles of a gas of volume V at pressure p and temperature T, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy U plus pV, where pV is the work done in pushing against the ambient (atmospheric) pressure.

In physics and statistical mechanics it may be more interesting to study the internal properties of a constant-volume system and therefore the internal energy is used.^{ [12] }^{ [13] } In chemistry, experiments are often conducted at constant atmospheric pressure, and the pressure–volume work represents a small, well-defined energy exchange with the atmosphere, so that Δ*H* is the appropriate expression for the heat of reaction. For a heat engine, the change in its enthalpy after a full cycle is equal to zero, since the final and initial state are equal.

In order to discuss the relation between the enthalpy increase and heat supply, we return to the first law for closed systems, with the physics sign convention: *dU* = *δQ* − *δW*, where the heat δQ is supplied by conduction, radiation, Joule heating. We apply it to the special case with a constant pressure at the surface. In this case the work is given by *p* *dV* (where p is the pressure at the surface, dV is the increase of the volume of the system). Cases of long range electromagnetic interaction require further state variables in their formulation, and are not considered here. In this case the first law reads:

Now,

So

If the system is under constant pressure, *dp* = 0 and consequently, the increase in enthalpy of the system is equal to the heat added:

This is why the now-obsolete term *heat content* was used in the 19th century.

In thermodynamics, one can calculate enthalpy by determining the requirements for creating a system from "nothingness"; the mechanical work required, pV, differs based upon the conditions that obtain during the creation of the thermodynamic system.

Energy must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure p remains constant; this is the pV term. The supplied energy must also provide the change in internal energy, U, which includes activation energies, ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. Together, these constitute the change in the enthalpy *U* + *pV*. For systems at constant pressure, with no external work done other than the pV work, the change in enthalpy is the heat received by the system.

For a simple system with a constant number of particles at constant pressure, the difference in enthalpy is the maximum amount of thermal energy derivable from an isobaric thermodynamic process.^{ [14] }

The total enthalpy of a system cannot be measured directly; the *enthalpy change* of a system is measured instead. Enthalpy change is defined by the following equation:

where

- Δ
*H*is the "enthalpy change", *H*_{f}is the final enthalpy of the system (in a chemical reaction, the enthalpy of the products or the system at equilibrium),*H*_{i}is the initial enthalpy of the system (in a chemical reaction, the enthalpy of the reactants).

For an exothermic reaction at constant pressure, the system's change in enthalpy, Δ*H*, is negative due to the products of the reaction having a smaller enthalpy than the reactants, and equals the heat released in the reaction if no electrical or shaft work is done. In other words, the overall decrease in enthalpy is achieved by the generation of heat.^{ [15] } Conversely, for a constant-pressure endothermic reaction, Δ*H* is positive and equal to the heat *absorbed* in the reaction.

From the definition of enthalpy as *H* = *U* + *pV*, the enthalpy change at constant pressure is Δ*H* = Δ*U* + *p* Δ*V*. However for most chemical reactions, the work term *p* Δ*V* is much smaller than the internal energy change Δ*U*, which is approximately equal to Δ*H*. As an example, for the combustion of carbon monoxide 2 CO(g) + O_{2}(g) → 2 CO_{2}(g), Δ*H* = −566.0 kJ and Δ*U* = −563.5 kJ.^{ [16] } Since the differences are so small, reaction enthalpies are often described as reaction energies and analyzed in terms of bond energies.

The specific enthalpy of a uniform system is defined as *h* = *H*/*m* where m is the mass of the system. The SI unit for specific enthalpy is joule per kilogram. It can be expressed in other specific quantities by *h* = *u* + *pv*, where u is the specific internal energy, p is the pressure, and v is specific volume, which is equal to 1/*ρ*, where ρ is the density.

An enthalpy change describes the change in enthalpy observed in the constituents of a thermodynamic system when undergoing a transformation or chemical reaction. It is the difference between the enthalpy after the process has completed, i.e. the enthalpy of the products assuming that the reaction goes to completion, and the initial enthalpy of the system, namely the reactants. These processes are specified solely by their initial and final states, so that the enthalpy change for the reverse is the negative of that for the forward process.

A common standard enthalpy change is the enthalpy of formation, which has been determined for a large number of substances. Enthalpy changes are routinely measured and compiled in chemical and physical reference works, such as the CRC Handbook of Chemistry and Physics. The following is a selection of enthalpy changes commonly recognized in thermodynamics.

When used in these recognized terms the qualifier *change* is usually dropped and the property is simply termed *enthalpy of 'process'*. Since these properties are often used as reference values it is very common to quote them for a standardized set of environmental parameters, or standard conditions, including:

- A pressure of one atmosphere (1 atm or 101.325 kPa) or 1 bar
- A temperature of 25 °C or 298.15 K
- A concentration of 1.0 M when the element or compound is present in solution
- Elements or compounds in their normal physical states, i.e. standard state

For such standardized values the name of the enthalpy is commonly prefixed with the term *standard*, e.g. *standard enthalpy of formation*.

Chemical properties:

- Enthalpy of reaction, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of substance reacts completely.
- Enthalpy of formation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a compound is formed from its elementary antecedents.
- Enthalpy of combustion, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a substance burns completely with oxygen.
- Enthalpy of hydrogenation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of an unsaturated compound reacts completely with an excess of hydrogen to form a saturated compound.
- Enthalpy of atomization, defined as the enthalpy change required to separate one mole of a substance into its constituent atoms completely.
- Enthalpy of neutralization, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of water is formed when an acid and a base react.
- Standard Enthalpy of solution, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a solute is dissolved completely in an excess of solvent, so that the solution is at infinite dilution.
- Standard enthalpy of Denaturation (biochemistry), defined as the enthalpy change required to denature one mole of compound.
- Enthalpy of hydration, defined as the enthalpy change observed when one mole of gaseous ions are completely dissolved in water forming one mole of aqueous ions.

Physical properties:

- Enthalpy of fusion, defined as the enthalpy change required to completely change the state of one mole of substance from solid to liquid.
- Enthalpy of vaporization, defined as the enthalpy change required to completely change the state of one mole of substance from liquid to gas.
- Enthalpy of sublimation, defined as the enthalpy change required to completely change the state of one mole of substance from solid to gas.
- Lattice enthalpy, defined as the energy required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction).
- Enthalpy of mixing, defined as the enthalpy change upon mixing of two (non-reacting) chemical substances.

In thermodynamic open systems, mass (of substances) may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: The increase in the internal energy of a system is equal to the amount of energy added to the system by mass flowing in and by heating, minus the amount lost by mass flowing out and in the form of work done by the system:

where *U*_{in} is the average internal energy entering the system, and *U*_{out} is the average internal energy leaving the system.

The region of space enclosed by the boundaries of the open system is usually called a control volume, and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of mass into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of mass out as if it were driving a piston of fluid. There are then two types of work performed: *flow work* described above, which is performed on the fluid (this is also often called *pV work*), and *shaft work*, which may be performed on some mechanical device such as a turbine or pump.

These two types of work are expressed in the equation

Substitution into the equation above for the control volume (cv) yields:

The definition of enthalpy, H, permits us to use this thermodynamic potential to account for both internal energy and pV work in fluids for open systems:

If we allow also the system boundary to move (e.g. due to moving pistons), we get a rather general form of the first law for open systems.^{ [17] } In terms of time derivatives it reads:

with sums over the various places k where heat is supplied, mass flows into the system, and boundaries are moving. The Ḣ_{k} terms represent enthalpy flows, which can be written as

with ṁ_{k} the mass flow and ṅ_{k} the molar flow at position k respectively. The term *dV*_{k}/*dt* represents the rate of change of the system volume at position k that results in pV power done by the system. The parameter *P* represents all other forms of power done by the system such as shaft power, but it can also be, say, electric power produced by an electrical power plant.

Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet.^{[ clarification needed ]} Otherwise, it has to be included in the enthalpy balance. During steady-state operation of a device (*see turbine, pump, and engine *), the average *dU*/*dt* may be set equal to zero. This yields a useful expression for the average power generation for these devices in the absence of chemical reactions:

where the angle brackets denote time averages. The technical importance of the enthalpy is directly related to its presence in the first law for open systems, as formulated above.

The enthalpy values of important substances can be obtained using commercial software. Practically all relevant material properties can be obtained either in tabular or in graphical form. There are many types of diagrams, such as *h*–*T* diagrams, which give the specific enthalpy as function of temperature for various pressures, and *h*–*p* diagrams, which give h as function of p for various T. One of the most common diagrams is the temperature–specific entropy diagram (*T*–*s* diagram). It gives the melting curve and saturated liquid and vapor values together with isobars and isenthalps. These diagrams are powerful tools in the hands of the thermal engineer.

The points **a** through **h** in the figure play a role in the discussion in this section.

Point T (K) p (bar) s (kJ/(kg K)) h (kJ/kg) **a**300 1 6.85 461 **b**380 2 6.85 530 **c**300 200 5.16 430 **d**270 1 6.79 430 **e**108 13 3.55 100 **f**77.2 1 3.75 100 **g**77.2 1 2.83 28 **h**77.2 1 5.41 230

Points **e** and **g** are saturated liquids, and point **h** is a saturated gas.

One of the simple applications of the concept of enthalpy is the so-called throttling process, also known as Joule–Thomson expansion. It concerns a steady adiabatic flow of a fluid through a flow resistance (valve, porous plug, or any other type of flow resistance) as shown in the figure. This process is very important, since it is at the heart of domestic refrigerators, where it is responsible for the temperature drop between ambient temperature and the interior of the refrigerator. It is also the final stage in many types of liquefiers.

For a steady state flow regime, the enthalpy of the system (dotted rectangle) has to be constant. Hence

Since the mass flow is constant, the specific enthalpies at the two sides of the flow resistance are the same:

that is, the enthalpy per unit mass does not change during the throttling. The consequences of this relation can be demonstrated using the *T*−*s* diagram above.

Point **c** is at 200 bar and room temperature (300 K). A Joule–Thomson expansion from 200 bar to 1 bar follows a curve of constant enthalpy of roughly 425 kJ/kg (not shown in the diagram) lying between the 400 and 450 kJ/kg isenthalps and ends in point **d**, which is at a temperature of about 270 K. Hence the expansion from 200 bar to 1 bar cools nitrogen from 300 K to 270 K. In the valve, there is a lot of friction, and a lot of entropy is produced, but still the final temperature is below the starting value.

Point **e** is chosen so that it is on the saturated liquid line with *h* = 100 kJ/kg. It corresponds roughly with *p* = 13 bar and *T* = 108 K. Throttling from this point to a pressure of 1 bar ends in the two-phase region (point **f**). This means that a mixture of gas and liquid leaves the throttling valve. Since the enthalpy is an extensive parameter, the enthalpy in **f** (*h*_{f}) is equal to the enthalpy in **g** (*h*_{g}) multiplied by the liquid fraction in **f** (*x*_{f}) plus the enthalpy in **h** (*h*_{h}) multiplied by the gas fraction in **f**(1 − *x*_{f}). So

With numbers: 100 = *x*_{f} × 28 + (1 − *x*_{f}) × 230, so *x*_{f} = 0.64. This means that the mass fraction of the liquid in the liquid–gas mixture that leaves the throttling valve is 64%.

A power P is applied e.g. as electrical power. If the compression is adiabatic, the gas temperature goes up. In the reversible case it would be at constant entropy, which corresponds with a vertical line in the *T*–*s* diagram. For example, compressing nitrogen from 1 bar (point **a**) to 2 bar (point **b**) would result in a temperature increase from 300 K to 380 K. In order to let the compressed gas exit at ambient temperature *T*_{a}, heat exchange, e.g. by cooling water, is necessary. In the ideal case the compression is isothermal. The average heat flow to the surroundings is Q̇. Since the system is in the steady state the first law gives

The minimal power needed for the compression is realized if the compression is reversible. In that case the second law of thermodynamics for open systems gives

Eliminating Q̇ gives for the minimal power

For example, compressing 1 kg of nitrogen from 1 bar to 200 bar costs at least (*h*_{c} − *h*_{a}) − *T*_{a}(*s*_{c} − *s*_{a}). With the data, obtained with the *T*–*s* diagram, we find a value of (430 − 461) − 300 × (5.16 − 6.85) = 476 kJ/kg.

The relation for the power can be further simplified by writing it as

With *dh* = *T* *ds* + *v* *dp*, this results in the final relation

The term *enthalpy* was coined relatively late in the history of thermodynamics, in the early 20th century. Energy was introduced in a modern sense by Thomas Young in 1802, while entropy was coined by Rudolf Clausius in 1865. *Energy* uses the root of the Greek word ἔργον (*ergon*), meaning "work", to express the idea of capacity to perform work. *Entropy* uses the Greek word τροπή (*tropē*) meaning *transformation* or *turning*. *Enthalpy* uses the root of the Greek word θάλπος (*thalpos*) "warmth, heat".^{ [19] }

The term expresses the obsolete concept of *heat content*,^{ [20] } as dH refers to the amount of heat gained in a process at constant pressure only,^{ [21] } but not in the general case when pressure is variable.^{ [22] } Josiah Willard Gibbs used the term "a heat function for constant pressure" for clarity.^{ [note 2] }

Introduction of the concept of "heat content" H is associated with Benoît Paul Émile Clapeyron and Rudolf Clausius (Clausius–Clapeyron relation, 1850).

The term *enthalpy* first appeared in print in 1909.^{ [23] } It is attributed to Heike Kamerlingh Onnes, who most likely introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris.^{ [24] } It gained currency only in the 1920s, notably with the * Mollier Steam Tables and Diagrams *, published in 1927.

Until the 1920s, the symbol H was used, somewhat inconsistently, for "heat" in general. The definition of H as strictly limited to enthalpy or "heat content at constant pressure" was formally proposed by Alfred W. Porter in 1922.^{ [25] }^{ [26] }

**Chemical thermodynamics** is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the *spontaneity* of processes.

The **thermodynamic free energy** is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

In chemistry, the **standard molar entropy** is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. These are often chosen to be the standard temperature and pressure.

Physical properties of materials and systems can often be categorized as being either **intensive** or **extensive**, according to how the property changes when the size of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems.

In thermodynamics, the **Gibbs free energy** is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions.

**Hess's law of constant heat summation**, also known simply as **Hess' law**, is a relationship in physical chemistry named after Germain Hess, a Swiss-born Russian chemist and physician who published it in 1840. The law states that the total enthalpy change during the complete course of a chemical reaction is independent of the sequence of steps taken.

A **thermodynamic potential** is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term *fundamental functions*.

In thermodynamics, the **Helmholtz free energy** is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.

The **internal energy** of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinetic energy. It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. It does not include the kinetic energy of motion of the system as a whole, or any external energies from surrounding force fields. The internal energy of an isolated system is constant, which is expressed as the law of conservation of energy, a foundation of the first law of thermodynamics. The internal energy is an extensive property.

The **standard enthalpy of reaction** for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. This can in turn be used to predict the total chemical bond energy liberated or bound during reaction, as long as the enthalpy of mixing is also accounted for.

In thermodynamics, an **isobaric process** is a type of thermodynamic process in which the pressure of the system stays constant: Δ*P* = 0. The heat transferred to the system does work, but also changes the internal energy (*U*) of the system. This article uses the physics sign convention for work, where positive work is work done by the system. Using this convention, by the first law of thermodynamics,

In thermodynamics, the **entropy of fusion** is the increase in entropy when melting a solid substance. This is almost always positive since the degree of disorder increases in the transition from an organized crystalline solid to the disorganized structure of a liquid; the only known exception is helium. It is denoted as and normally expressed in joules per mole-kelvin, J/(mol·K).

Thermodynamics is expressed by a mathematical framework of *thermodynamic equations* which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

In thermodynamics, **work** is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. An exchange of energy is facilitated by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings, or vice versa. In the surroundings, this mechanical work can lift a weight, for example.

The **Van 't Hoff equation** relates the change in the equilibrium constant, *K*_{eq}, of a chemical reaction to the change in temperature, *T*, given the standard enthalpy change, Δ_{r}*H*^{⊖}, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book *Études de Dynamique chimique*.

In classical thermodynamics, **entropy** is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word τρoπή (*transformation*) to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system.

In thermodynamics, **entropy** is a numerical quantity that shows that many physical processes can go in only one direction in time. For example, you can pour cream into coffee and mix it, but you cannot "unmix" it; you can burn a piece of wood, but you cannot "unburn" it. The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder. A more physical interpretation of thermodynamic entropy refers to spread of energy or matter, or to extent and diversity of microscopic motion.

**Thermodynamic databases** contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.

In thermodynamics, **heat** is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not *contain* heat. Nevertheless, the term is also often used to refer to the thermal energy contained in a system as a component of its internal energy and that is reflected in the temperature of the system. For both uses of the term, heat is a form of energy.

**Entropy production** is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners.

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*Heat and Thermodynamics*(5th ed.). New York, NY: McGraw-Hill. p. 275. - ↑ Van Wylen, G. J.; Sonntag, R. E. (1985). "Section 5.5".
*Fundamentals of Classical Thermodynamics*(3rd ed.). New York: John Wiley & Sons. ISBN 978-0-471-82933-1. - ↑ Atkins, Peter; de Paula, Julio (2006).
*Atkins' Physical Chemistry*(8th ed.). W.H.Freeman. p. 51. ISBN 0-7167-8759-8. - ↑ Laidler, Keith J.; Meiser, John H. (1999).
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- ↑ Reif, F. (1967).
*Statistical Physics*. London: McGraw-Hill. - ↑ Kittel, C.; Kroemer, H. (1980).
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*General Chemistry*(8th ed.). Prentice Hall. pp. 237–238. ISBN 978-0-13-014329-7. - ↑ Moran, M. J.; Shapiro, H. N. (2006).
*Fundamentals of Engineering Thermodynamics*(5th ed.). John Wiley & Sons. p. 129. ISBN 9780470030370. - ↑ Figure composed with data obtained with RefProp, NIST Standard Reference Database 23.
- ↑ θάλπος in
*A Greek–English Lexicon*. - ↑ Howard (2002) quotes J. R. Partington in
*An Advanced Treatise on Physical Chemistry*(1949) as saying that the function*H*was "usually called the heat content". - ↑ Tinoco, Ignacio Jr.; Sauer, Kenneth; Wang, James C. (1995).
*Physical Chemistry*(3rd ed.). Prentice-Hall. p. 41. ISBN 978-0-13-186545-7. - ↑ Laidler, Keith J.; Meiser, John H. (1982).
*Physical Chemistry*. Benjamin/Cummings. p. 53. ISBN 978-0-8053-5682-3. - ↑ Dalton, J. P. (1909). "Researches on the Joule–Kelvin-effect, especially at low temperatures. I. Calculations for hydrogen".
*Proceedings of the Section of Sciences (Koninklijke Akademie van Wetenschappen te Amsterdam [Royal Academy of Sciences at Amsterdam])*. 11 (part 2): 863–873. Bibcode:1908KNAB...11..863D. ; see p. 864, footnote (1). - ↑ See:
- Laidler, Keith (1995).
*The World of Physical Chemistry*. Oxford University Press. p. 110. - Van Ness, Hendrick C. (2003). "
*H*Is for Enthalpy".*Journal of Chemical Education*.**80**(6): 486. Bibcode:2003JChEd..80..486V. doi: 10.1021/ed080p486.1 .

- Laidler, Keith (1995).
- ↑ Porter, Alfred W. (1922). "The generation and utilisation of cold. A general discussion".
*Transactions of the Faraday Society*.**18**: 139–143. doi:10.1039/tf9221800139.; see p. 140. - ↑ Howard, Irmgard (2002). "
*H*Is for Enthalpy, Thanks to Heike Kamerlingh Onnes and Alfred W. Porter".*Journal of Chemical Education*.**79**(6): 697. Bibcode:2002JChEd..79..697H. doi:10.1021/ed079p697.

- Dalton, J.P. (1909). "Researches on the Joule–Kelvin effect, especially at low temperatures. I. Calculations for hydrogen" (PDF).
*KNAW Proceedings*.**11**: 863–873. Bibcode:1908KNAB...11..863D. - Haase, R. (1971). Jost, W. (ed.).
*Physical Chemistry: An Advanced Treatise*. New York: Academic. p. 29. - Gibbs, J. W.
*The Collected Works of J. Willard Gibbs, Vol. I*(1948 ed.). New Haven, CT: Yale University Press. p. 88. - Howard, I. K. (2002). "
*H*Is for Enthalpy, Thanks to Heike Kamerlingh Onnes and Alfred W. Porter".*J. Chem. Educ.***79**(6): 697–698. Bibcode:2002JChEd..79..697H. doi:10.1021/ed079p697. - Laidler, K. (1995).
*The World of Physical Chemistry*. Oxford: Oxford University Press. p. 110. ISBN 978-0-19-855597-1. - Kittel, C.; Kroemer, H. (1980).
*Thermal Physics*. New York: S. R. Furphy & Co. p. 246. - DeHoff, R. (2006).
*Thermodynamics in Materials Science*. CRC Press. ISBN 9780849340659.

- Enthalpy – Eric Weisstein's World of Physics
- Enthalpy – Georgia State University
- Enthalpy example calculations – Texas A&M University Chemistry Department

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