Enthalpy

Statistical mechanics

$S = k_B \, \ln\Omega$

Statistical thermodynamics
Kinetic theory

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In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H, h, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure and entropy. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. System (from Latin systēma, in turn from Greek systēma is a set of interacting or interdependent Entities, real or abstract A Closed system is a System in the state of being isolated from the environment In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy

The term enthalpy was composed of the prefix en-, meaning to "put into" and the Greek word -thalpein, meaning "to heat", although the original definition is thought to have stemmed from the word "enthalpos" (ἐνθάλπος). Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly ^[1]

1 History
- 1.1 Original definition
2 Application and extended formula
3 Standard enthalpy changes
- 3.1 Definitions
  - 3.1.1 Chemical Properties
  - 3.1.2 Physical Properties
4 Specific enthalpy
5 See also
6 Notes
7 References
8 External links

History

Over the history of thermodynamics, several terms have been used to denote what is now known as the enthalpy of a system. The history of thermodynamics is a fundamental strand in the History of physics, the History of chemistry, and the History of science in general Originally, it was thought that the word "enthalpy" was created by Benoit Paul Émile Clapeyron and Rudolf Clausius through the publishing of the Clausius-Clapeyron relation in "The Mollier Steam Tables and Diagrams" in 1827, but it was later published that the earliest recording of the word was in 1875, by Josiah Willard Gibbs in the publication "Physical Chemistry: an Advanced Treatise"^[2], although it is not referenced in Gibbs' works directly^[3]. Benoît Paul Émile Clapeyron (26 February 1799 - 28 January 1864 was a French Engineer and Physicist, one of the founders of Thermodynamics Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist The Clausius-Clapeyron relation, named after Rudolf Clausius and Émile Clapeyron, is a way of characterizing the Phase transition between two phases of Year 1827 ( MDCCCXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common Year 1875 ( MDCCCLXXV) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar (or a Common Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist In 1909, Keith Landler discussed Gibbs' work on the 'heat function for constant pressure' and noted that Heike Kamerlingh Onnes had coined its modern name from the Greek word "enthalpos" (ενθαλπος) meaning "to put heat into. Year 1909 ( MCMIX) was a Common year starting on Friday (link will display full calendar of the Gregorian calendar (or a Common year starting Heike Kamerlingh Onnes ( September 21, 1853 &ndash February 21, 1926) was a Dutch Physicist. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly " ^[1]

Original definition

This is the heat change which occurs when 1 mol of a substance reacts completely with oxygen to form products at 298 K and 1 atm. The function H was introduced by the Dutch physicist Heike Kamerlingh Onnes in early 20th century in the following form:

$H = E + pV,\,$

where E represents the energy of the system. Heike Kamerlingh Onnes ( September 21, 1853 &ndash February 21, 1926) was a Dutch Physicist. In the absence of an external field, the enthalpy may be defined, as it is generally known, by:

$H = U + pV,\,$

where (all units given in SI)

H is the enthalpy (joules)
U is the internal energy, (joules)
p is the pressure of the system, (pascals)
V is the volume, (cubic metres)

Application and extended formula

Overview

In terms of thermodynamics, enthalpy can be calculated by determining the requirements for creating a system from "nothingness"; the mechanical work required, $p V$ differs, based upon the constancy of conditions present at the creation of the thermodynamic system. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically CM3 redirects here If you were looking for the 3rd game in the Cooking Mama series abbreviated as CM3 see here. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration

Internal energy, $U$ , must be supplied to remove particles from a surrounding in order to allow space for the creation of a system, providing that environmental variables, such as pressure ( $p$ ) remain constant. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes This internal energy also includes the energy required for activation and the breaking of bonded compounds into gaseous species. In Chemistry, activation energy, also called midnight energy, is a term introduced in 1889 by the Swedish scientist Svante Arrhenius, that is defined

This process is calculated within enthalpy calculations as $U + p V$ , to label the amount of energy or work required to "set aside space for" and "create" the system; describing the work done by both the reaction or formation of systems, and the surroundings. For systems at constant pressure, the change in enthalpy is the heat received by the system plus the non-mechanical work that has been done.

Therefore, the change in enthalpy can be devised or represented without the need for compressive or expansive mechanics; for a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.

The term $p$ $V$ is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.

Relationships

As an expansion of the first law of thermodynamics, enthalpy can be related to several other thermodynamic formulae. In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy. As with the original definition of the first law;

$\mathrm{d}U = \delta Q + \delta W\,$

Where, as defined by the law;

d U

represents the infinitesimal increase of the systematic or internal energy. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration

δ Q

represents the infinitesimal amount of energy attributed or added to the system.

δ W

represents the infinitesimal amount of energy acted out by the system on the surroundings.

As a differentiating expression, the value of H can be defined as

$\mathrm{d}H = \mathrm{d}U + (p\,\mathrm{d}V + V\mathrm{d}p) \!$

$= (\delta Q - p\,\mathrm{d}V) + (p\,\mathrm{d}V + V\mathrm{d}p) \!$

$= \delta Q +V\mathrm{d}p = T\mathrm{d}S + V\mathrm{d}p \!$

Where

$δ$ represents the inexact differential. In Thermodynamics, an inexact differential or imperfect differential is any quantity particularly Heat Q and work W that are not State	$U$ is the internal energy,
$δ Q = T d S$ is the energy added by heating during a reversible process,	$δ W = p d V$ is the work done by the system in a reversible process. In Thermodynamics, the internal energy of a Thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes For articles on other forms of reversibility including reversibility of microscopic dynamics see Reversibility (disambiguation.
$d S$ is the increase in entropy (joules per kelvin),	$p$ is the constant pressure
$d V$ is an infinitesimal volume	$T$ is the temperature (kelvins)

For a process that is not reversible, the above equation expressing dH in terms of dS and dP still holds because H is a thermodynamic state variable that can be uniquely specified by S and P. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have We thus have in general:

$\mathrm{d}H = T\mathrm{d}S+V\mathrm{d}p\,$

It is seen that, if a thermodynamic process is isobaric (i. e. , occurs at constant pressure), then $d p$ is zero and thus

$\mathrm{d}H = T\mathrm{d}S\geq \delta Q \,$

The difference in enthalpy is the maximum thermal energy attainable from the system in an isobaric process. An isobaric process is a Thermodynamic process in which the pressure stays constant \Delta p = 0 The term derives from the Greek isos "equal" This explains why it is sometimes called the heat content. That is, the integral of $d H$ over any isobar in state space is the maximum thermal energy attainable from the system.

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. In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical The differential statement for $d H$ is then:

$dH = T\mathrm{d}S+V\mathrm{d}p + \sum_i \mu_i \,\mathrm{d}N_i\,$

where $μ i$ is the chemical potential for an i-type particle, and $N i$ is the number of such particles. It is seen that, not only must the $V d p$ term be set to zero by requiring the pressures of the initial and final states to be the same, but the $μ i d N i$ terms must be zero as well, by requiring that the particle numbers remain unchanged. Any further generalization will add even more terms whose extensive differential term must be set to zero in order for the interpretation of the enthalpy to hold.

Heats of reaction

The total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration Enthalpy change is defined by the following equation:

$\Delta H = H_\mathrm{final} - H_\mathrm{initial} \,$

where

ΔH is the enthalpy change

H_final is the final enthalpy of the system, measured in joules. In a chemical reaction, H_final is the enthalpy of the products.

H_initial is the initial enthalpy of the system, measured in joules. In a chemical reaction, H_initial is the enthalpy of the reactants.

For an exothermic reaction at constant pressure, the system's change in enthalpy is equal to the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. An exothermic reaction is a Chemical reaction that releases Heat. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In a similar manner, for an endothermic reaction, the system's change in enthalpy is equal to the energy absorbed in the reaction, including the energy lost by the system and gained from compression from its surroundings. In Thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs Energy in the form of Heat. A relatively easy way to determine whether or not a reaction is exothermic or endothermic is to determine the sign of ΔH. If ΔH is positive, the reaction is endothermic, that is heat is absorbed by the system due to the products of the reaction having a greater enthalpy than the reactants. On the other hand if ΔH is negative, the reaction is exothermic, that is the overall decrease in enthalpy is achieved by the generation of heat.

Although enthalpy is commonly used in engineering and science, it is impossible to measure directly, as enthalpy has no datum (reference point). Therefore enthalpy can only accurately be used in a closed system. A Closed system is a System in the state of being isolated from the environment However, few real world applications exist in closed isolation, and it is for this reason that two or more closed systems cannot be compared using enthalpy as a basis, although sometimes this is done erroneously.

Open systems

In thermodynamic open systems, matter may flow in and out of the system boundaries. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " An open system is a state of a System, in which a system continuously interacts with its environment 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 matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. The first law for open systems is given by:

$\mathrm{d}U= \mathrm{d}U_{in}-\mathrm{d}U_{out}+\delta Q-\delta W\,$

where U_in is the average internal energy entering the system and U_out is the average internal energy leaving the system

During steady, continuous operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added. A Unit operation is considered to be at a steady state with respect to an operation variable if that variable does not change with time

The region of space enclosed by open system boundaries is usually called a control volume, and it may or may not correspond to physical walls. In Fluid mechanics and Thermodynamics, a control volume is a mathematical abstraction employed in the process of creating Mathematical models 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 matter 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 matter 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 $p V$ work) and shaft work which may be performed on some mechanical device.

These two types of work are expressed in the equation:

$\delta W=\mathrm{d}(p_{out}V_{out})-\mathrm{d}(p_{in}V_{in})+\delta W_{shaft}.\,$

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

$\mathrm{d}U_{cv}=\mathrm{d}U_{in}+\mathrm{d}(p_{in}V_{in}) - \mathrm{d}U_{out}-\mathrm{d}(p_{out}V_{out})+\delta Q-\delta W_{shaft}.\,$

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

$\mathrm{d}U_{cv}=\mathrm{d}H_{in}-\mathrm{d}H_{out}+\delta Q-\delta W_{shaft}.\,$

During steady-state operation of a device (see turbine, pump, and engine), the expression above may be set equal to zero. A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. A Unit operation is considered to be at a steady state with respect to an operation variable if that variable does not change with time A turbine is a rotary Engine that extracts Energy from a Fluid flow For information on Wikipedia project-related discussions see WikipediaVillage pump. An engine is a mechanical device that produces some form of output from a given input This yields a useful expression for the power generation or requirement for these devices in the absence of chemical reactions:

$\frac{\delta W_{shaft}}{\mathrm{d}t}=\frac{\mathrm{d}H_{in}}{\mathrm{d}t}- \frac{\mathrm{d}H_{out}}{\mathrm{d}t}+\frac{\delta Q}{\mathrm{d}t}. \,$

This expression is described by the diagram above. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for

Standard enthalpy changes

Standard enthalpy changes describe the change in enthalpy observed in the constituents of a thermodynamic system when going between different states under standard conditions. The standard enthalpy change of vaporization, for example gives the enthalpy change when going from liquid to gas. These enthalpies are reversible; the enthalpy change of going from gas to liquid is the negative of the enthalpy change of vaporization. A common standard enthalpy change is the standard enthalpy change of formation, which has been determined for a large number of substances. The standard enthalpy of formation or "standard heat of formation" of a compound is the change of Enthalpy that accompanies the formation of 1 mole of a The enthalpy change of any reaction under any conditions can be computed, given the standard enthalpy change of formation of all of the reactants and products. A product is a substance that forms as a result of a Biological - or Chemical reaction.

Definitions

Chemical Properties

Standard enthalpy change of reaction

“

Standard enthalpy change of reaction is defined as the enthalpy change observed in a constituent of a thermodynamic system when, one mole of substance reacts completely under standard conditions. The standard enthalpy change of reaction (denoted ΔH ° or ΔH o is the Enthalpy change that occurs in a system when one mole of matter The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this

”

Standard enthalpy change of formation

“

Standard enthalpy change of formation is 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 under standard conditions. The standard enthalpy of formation or "standard heat of formation" of a compound is the change of Enthalpy that accompanies the formation of 1 mole of a In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made

”

Standard enthalpy change of combustion

“

Standard enthalpy of combustion is defined as the enthalpy change observed in a constituent of a thermodynamic system, when one mole of a substance combusts completely with oxygen under standard conditions. The standard enthalpy of combustion is the Enthalpy change when one mole of a substance completely reacts with oxygen under standard thermodynamic conditions (although

”

Standard enthalpy change of hydrogenation

“

Standard enthalpy of hydrogenation is 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 under standard conditions to form a saturated compound. The standard enthalpy of formation or "standard heat of formation" of a compound is the change of Enthalpy that accompanies the formation of 1 mole of a

”

Standard enthalpy change of atomization

“

Standard enthalpy of atomization is defined as the enthalpy change required to atomize one mole of compound completely under standard conditions. The enthalpy of atomization (also standard enthalpy of atomisation - UK spelling is the Enthalpy change that accompanies the total separation of all atoms in a chemical substance

”

Physical Properties

Standard enthalpy change of solution

“

Standard enthalpy of solution is defined as the enthalpy change observed in a constituent of a thermodynamic system, when one mole of an solute is dissolved completely in an excess of solvent under standard conditions. The enthalpy of solution (or enthalpy of dissolution) is the Enthalpy change associated with the dissolution of a substance in a Solvent at constant pressure

”

Standard enthalpy change of fusion

“

Standard enthalpy of fusion is defined as the enthalpy change required to completely change the state of one mole of substance between solid and liquid states under standard conditions. The standard Enthalpy of fusion (symbol \Delta{}H_{fus} also known as the heat of fusion or specific melting heat, is the amount of

”

Standard enthalpy change of vapourization

“

Standard enthalpy of vapourization is defined as the enthalpy change required to completely change the state of one mole of substance between liquid and gaseous states under standard conditions. The enthalpy of vaporization, (symbol \Delta{}_{v}H also known as the heat of vaporization or heat of evaporation, is the Energy required

”

Standard enthalpy change of sublimation

“

Standard enthalpy of sublimation is defined as the enthalpy change required to completely change the state of one mole of substance between solid and gaseous states under standard conditions. The heat of sublimation, or Enthalpy of sublimation, is defined as the Heat required to sublime one mole of the substance at a given

”

Standard enthalpy change of denaturation

“

Standard enthalpy of denaturation is defined as the enthalpy change required to denature one mole of compound under standard conditions. Denaturation is a process in which Proteins or Nucleic acids lose their structure (tertiary structure by application of some external stress or compound for

”

Lattice enthalpy

“

Lattice enthalpy is defined as the enthalpy required required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction) under standard conditions. The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound

”

Specific enthalpy

The specific enthalpy of a working mass is a property of that mass used in thermodynamics, defined as $h=u+p \cdot v$ where u is the specific internal energy, p is the pressure, and v is specific volume. Working mass is a mass against which a system operates in order to produce Acceleration. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " In other words, $h = H / m$ where $m$ is the mass of the system. The SI unit for specific enthalpy is joules per kilogram.

Notes

^ ^a ^b The World of Chemistry noted that whilst ruminating on the origin being credited to Gibbs, the original word was created by Onnes, who had specified its derivation. Calorimetry is the Science of measuring the Heat of Chemical A calorimeter is a device used for Calorimetry, the Science of measuring the heat of Chemical reactions or Physical changes as well as Heat In Thermodynamics, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Hess's law is a law of Physical chemistry named for Germain Hess 's expansion of the Hess Cycle and used to predict the enthalpy change and conservation of energy (denoted An isenthalpic process is one that proceeds without any change in Enthalpy, H; or specific enthalpy, h. Thermodynamic databases contain information about thermodynamic properties for substances the most important being Enthalpy, Entropy, and
^ Physical Chemistry: An Advanced Treatise States that the original creator of the word was Josiah Willard Gibbs, who noted "the familiar definition of enthalpy as introduced by Gibbs in 1875 (‘heat function for constant pressure’)”"
^ The Collected Works of J. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist Willard Gibbs, Vol. I do not contain reference to the word enthalpy, but rather reference the heat function for constant pressure.

References

Haase, R. In Physical Chemistry: An Advanced Treatise; Jost, W. , Ed. ; Academic: New York, 1971; p 29.
Gibbs, J. W. In The Collected Works of J. Willard Gibbs, Vol. I; Yale University Press: New Haven, CT, reprinted 1948; p 88.
Laidler, K. The World of Physical Chemistry; Oxford University Press: Oxford, 1995; p 110.
C. Kittel, H. Kroemer In Thermal Physics; W. H. Freeman and Company, New York, 1980; p246

External links

Enthalpy - Eric Weisstein's World of Physics
Enthalpy - Georgia State University
Enthalpy - KnowAllAbout. com
Enthalpy (example calculations) - Texas A&M University (Chemistry Department)
Enthalpy - Water and Steam Enthalpy

Dictionary

-noun

(physics) In thermodynamics, a measure of the heat content of a chemical or physical system.

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