Enthalpy: Difference between revisions
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= | {{Thermodynamics|expanded=Potentials}} | ||
'''Enthalpy''' is a measure of the total [[energy]] of a [[thermodynamic system]]. It includes the system's [[internal energy]] and [[thermodynamic potential]] (a [[state function]]), as well as its [[volume]] and [[pressure]] (the energy required to "make room for it" by displacing its [[environment (systems)|environment]], which is an [[extensive]] quantity). The unit of measurement for enthalpy in the [[International System of Units]] (SI) is the [[joule]], but other historical, conventional units are still in use, such as the [[British thermal unit]] and the [[calorie]]. | |||
The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of [[energy transfer]]. Enthalpy change accounts for energy transferred to the environment at constant pressure through expansion or heating. | |||
The total enthalpy, ''H'', of a system cannot be measured directly. The same situation exists in classical mechanics: only a change or difference in energy carries physical meaning. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; therefore what we measure is the change in enthalpy, Δ''H. ''The change Δ''H'' is positive in [[endothermic]] reactions, and negative in heat-releasing [[exothermic]] processes. Δ''H'' of a system is equal to the sum of non-mechanical work done on it and the heat supplied to it. | |||
For processes under constant pressure, Δ''H'' is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.<ref>G.J. Van Wylen and R.E. Sonntag (1985), ''Fundamentals of Classical Thermodynamics'', Section 5.5 (3rd edition), John Wiley & Sons Inc. New York, NY. ISBN 0-471-82933-1</ref> This means that the change in enthalpy under such conditions is the heat absorbed (or released) by the material through a chemical reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume [[standard state]]: most commonly 1 bar pressure. Standard state does not, strictly speaking, specify a temperature (see [[standard state]]), but expressions for enthalpy generally reference the standard heat of formation at 25 °C. | |||
Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike [[entropy]] and [[Gibbs free energy|Gibbs energy]]. Real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses. | |||
== | ==Origins== | ||
The word ''enthalpy'' is based on the Greek [[noun]] ''enthalpos'' (ἔνθαλπος), which means ''heating''. It comes from the [[Classical Greek language|Classical Greek]] prefix [[wikt:ἐν|ἐν-]], ''en-'', meaning ''to put into'', and the verb [[wikt:θάλπω|θάλπειν]], ''thalpein'', meaning "to heat". The word ''enthalpy'' is often incorrectly attributed{{Citation needed|date=September 2010}} to [[Benoît Paul Émile Clapeyron]] and [[Rudolf Clausius]] through the 1850 publication of their [[Clausius-Clapeyron relation]]. This misconception was popularized by the 1927 publication of ''[[enthalpy–entropy chart|The Mollier Steam Tables and Diagrams]]''. However, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyron's death. | |||
== | The earliest writings to contain the concept of enthalpy did not appear until 1875,<ref>{{Cite book | ||
|last1=Henderson|first1=Douglas|last2=Eyring|first2=Henry|last3=Jost|first3=Wilhelm | |||
|title=Physical Chemistry: An Advanced Treatise | |||
|publisher=Academic Press|year=1967|page=29 | |||
}}</ref> | |||
when [[Josiah Willard Gibbs]] introduced "a heat function for constant pressure". However, Gibbs did not use the word "enthalpy" in his writings.<ref group=note>''The Collected Works of J. Willard Gibbs, Vol. I'' do not contain reference to the word enthalpy, but rather reference the heat function for constant pressure.</ref> | |||
The actual word first appears in the scientific literature in a 1909 publication by J. P. Dalton. According to that publication, [[Heike Kamerlingh Onnes]] (1853-1926) actually coined the word.<ref>{{Cite book|last=Laidler|first1=Keith|authorlink=Keith J. Laidler|title=The World of Physical Chemistry|publisher=Oxford University Press|year=1995|page=110}}</ref> | |||
Over the years, many different symbols were used to denote enthalpy. It was not until 1922 that Alfred W. Porter proposed the symbol "H" as the accepted standard,<ref>{{Cite journal|doi=10.1021/ed079p697 |last=Howard|first=Irmgard |year=2002|title=H Is for Enthalpy, Thanks to Heike Kamerlingh Onnes and Alfred W. Porter|journal=Journal of Chemical Education|publisher=ACS Publications|volume=79|issue=6|pages=697|url=http://pubs.acs.org/doi/abs/10.1021/ed079p697|bibcode = 2002JChEd..79..697H }}</ref> thus finalizing the terminology still in use today. | |||
==Formal definition== | |||
The enthalpy of a homogeneous system is defined as:<ref>E.A. Guggenheim, Thermodynamics, North-Holland Publisching Company, Amsterdam, 1959</ref><ref>{{Cite book|author=Zumdahl, Steven S.|chapter=Thermochemistry|title=Chemistry|publisher=Cengage Learning|year=2008|isbn=978-0-547-12532-9|page=243|url=http://books.google.com/books?id=LLWkH82PNbYC&pg=PA243}}</ref> | |||
:<math>H = U + p V\,</math> | |||
where | |||
:''H'' is the enthalpy of the system | |||
:''U'' is the [[internal energy]] of the system | |||
:''p'' is the [[pressure]] of the system | |||
:''V'' is the [[Volume (thermodynamics)|volume]] of the system. | |||
The enthalpy is an [[extensive property]]. This means that, for homogeneous systems, the enthalpy is proportional to the size of the system. It is convenient to introduce the specific enthalpy ''h'' =''H/m'' where ''m'' is the mass of the system, or the molar enthalpy ''H''<sub>m</sub> = ''H/n'', where ''n'' is the number of moles (''h'' and ''H''<sub>m</sub> are [[intensive properties]]). For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems | |||
:<math>H = \Sigma_k H_k</math> | |||
where the label ''k'' refers to the various subsystems. In case of continuously varying ''p'', ''T'', and/or composition the summation becomes an integral: | |||
:<math>H = \int \rho h \mathrm{d}V,</math> | |||
where ''ρ'' is the density. | |||
The enthalpy ''H''(''S,p'') of homogeneous systems can be derived as a characteristic function of the entropy ''S'' and the pressure ''p'' as follows: we start from the [[first law of thermodynamics]] for closed systems for an infinitesimal process | |||
:<math>\mathrm{d} U = \delta Q -\delta W.</math> | |||
Here, δ''Q'' is a small amount of heat added to the system and δ''W'' a small amount of work performed by the system. In a homogeneous system only reversible processes can take place so the [[second law of thermodynamics]] gives δ''Q'' = ''T''d''S'' with ''T'' the [[absolute temperature]] of the system. Furthermore, if only pV work is done, δ''W'' = ''p''d''V''. As a result | |||
:<math>\mathrm{d} U = T\mathrm{d}S-p\mathrm{d}V.</math> | |||
Adding d(''pV'') to both sides of this expression gives | |||
:<math>\mathrm{d}U+ \mathrm{d}(pV) = T\mathrm{d}S-p\mathrm{d}V+ \mathrm{d}(pV)</math> | |||
or | |||
:<math>\mathrm{d} (U + pV) = T\mathrm{d}S+V\mathrm{d}p.</math> | |||
So | |||
:<math>\mathrm{d} H(S,p) = T\mathrm{d} S + V \mathrm{d} p.</math> | |||
==Other expressions== | |||
The expression of d''H'' in terms of entropy and pressure may be unfamiliar to many readers. However, there are expressions in terms of more familiar variables such as temperature and pressure<ref>Guggenheim, p. 88</ref><ref>M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.511.</ref> | |||
<math>\mathrm{d}H = C_p\mathrm{d}T+V(1-\alpha T)\mathrm{d}p.</math> | |||
Here ''C''<sub>p</sub> is the heat capacity at constant pressure and ''α'' is the coefficient of (cubic) thermal expansion | |||
<math>\alpha=\frac{1}{V}\left(\frac{\part V}{\part T}\right)_p.</math> | |||
With this expression one can, in principle, determine the enthalpy if ''C''<sub>p</sub> and ''V'' are known as functions of ''p'' and ''T''. | |||
Notice that for an [[ideal gas]], <math>\alpha T = 1</math>,<ref group=note><math>\alpha T=\frac{T}{V}\left(\frac{\part n R T / P}{\part T}\right)_p = \frac{nRT}{PV} = 1</math></ref> so that: | |||
<math>\mathrm{d}H = C_p\mathrm{d}T</math> | |||
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 d''H'' then becomes: | |||
:<math>\mathrm{d}H = T\mathrm{d}S+V\mathrm{d}p + \sum_i \mu_i \mathrm{d}N_i</math> | |||
where ''μ''<sub>''i''</sub> is the chemical potential per particle for an ''i''-type particle, and ''N''<sub>''i''</sub> is the number of such particles. The last term can also be written as ''μ''<sub>i</sub>d''n''<sub>''i''</sub> (with d''n''<sub>''i''</sub> the number of moles of component ''i'' added to the system and, in this case, ''μ''<sub>i</sub> the molar chemical potential) or as ''μ''<sub>i</sub>d''m''<sub>''i''</sub> (with d''m''<sub>''i''</sub> the mass of component ''i'' added to the system and, in this case, ''μ''<sub>i</sub> the specific chemical potential). | |||
==Enthalpy versus internal energy== | |||
The ''U'' term can be interpreted as the energy required to create the system, and the ''pV'' term as the energy that would be required to "make room" for the system if the pressure of the environment remained constant. When a system, for example, ''n'' [[Mole (unit)|moles]] of a gas of [[Volume (thermodynamics)|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 (physics)|work]] done in pushing against the ambient (atmospheric) pressure. | |||
In basic [[physics]] and [[statistical mechanics]] it may be more interesting to study the internal properties of the system and therefore the internal energy is used.<ref>F. Reif Statistical physics McGraw-Hill, London (1967)</ref><ref>C. Kittel and H. Kroemer Thermal physics Freeman London (1980)</ref> In basic [[chemistry]], experiments are often conducted at [[atmospheric pressure]] and ''H'' is therefore more useful for reaction energy calculations. Furthermore the enthalpy is the workhorse of engineering thermodynamics as we will see later. | |||
== Relationship to heat == | |||
In order to discuss the relation between the enthalpy increase and heat supply we return to the first law for closed systems: d''U'' = δ''Q'' - δ''W''. We apply it to the special case that the pressure at the surface is uniform. In this case the work term can be split in two contributions, the so-called pV work, given by ''p''d''V'' (where here ''p'' is the pressure at the surface, d''V'' is the increase of the volume of the system) and other types of work δ''W'' ' such as by a shaft or by electromagnetic interaction. So we write δ''W'' = ''p''d''V''+δ''W'' '. In this case the first law reads | |||
:<math>\mathrm{d} U = \delta Q -p\mathrm{d}V-\delta W^\prime</math> | |||
or | |||
:<math>\mathrm{d} H = \delta Q +V\mathrm{d}p-\delta W^\prime.</math> | |||
From this relation we see that the increase in enthalpy of a system is equal to the added [[heat]] | |||
:<math>\mathrm{d} H = \delta Q </math> | |||
provided that the system is under [[isobaric system|constant pressure]] (d''p'' = 0) and that the only work done by the system is expansion work (δ''W'' ' = 0)<ref>{{cite book|authors=Ebbing, Darrel & Gammon, Steven|title=General Chemistry|publisher=Cengage Learning|year=2010|isbn=978-0-538-49752-7|page=231|url=http://books.google.com/books?id=8_7iGj4QLR4C&pg=PA231}}</ref> | |||
==Applications== | |||
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 constancy of conditions present at the creation of the [[thermodynamic system]]. | |||
[[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. This internal energy also includes the energy required for [[activation energy|activation]] and the breaking of bonded compounds into gaseous species. | |||
This process is calculated within enthalpy calculations as ''U'' + ''pV'', 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. | |||
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 ''pV'' is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system. | |||
===Heat of reaction=== | |||
The total enthalpy of a system cannot be measured directly; the ''enthalpy change'' of a [[system (thermodynamics)|system]] is measured instead. Enthalpy change is defined by the following equation: | |||
<math>\Delta</math><math>H</math> <math>=</math> <math>H_f</math> <math>-</math> <math>H_i</math> | |||
where | |||
<math>\Delta H</math> is the "enthalpy change" | |||
<math>H_f</math> is the final enthalpy of the system, expressed in joules. In a chemical reaction,<math>H_f</math> is the enthalpy of the products. | |||
<math>H_i</math> is the initial enthalpy of the system, expressed in joules. In a chemical reaction,<math>H_i</math> is the enthalpy of the reactants. | |||
For an [[exothermic reaction|exothermic]] [[chemical reaction|reaction]] at constant [[pressure]], the system's change in enthalpy equals the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. 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. A relatively easy way to determine whether or not a reaction is exothermic or endothermic is to determine the sign of Δ''H''. If Δ''H'' 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 Δ''H'' 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]]. However, few real-world applications exist in closed isolation, and it is for this reason that two or more closed systems cannot correctly be compared using enthalpy as a basis. | |||
===Specific enthalpy=== | |||
As noted before, 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. | |||
===Enthalpy changes=== | |||
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 [[Product (chemistry)|products]], and the initial enthalpy of the system, i.e. the reactants. These processes are reversible and the enthalpy for the reverse process is the negative value of the forward change. | |||
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 [[temperature]] of 25 °C or 298 K, | |||
* A [[pressure]] of one atmosphere (1 atm or 101.325 kPa), | |||
* 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 atomize one mole of compound 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 between solid and liquid states. | |||
* [[Enthalpy of vaporization]], defined as the enthalpy change required to completely change the state of one mole of substance between liquid and gaseous states. | |||
* [[Enthalpy of sublimation]], defined as the enthalpy change required to completely change the state of one mole of substance between solid and gaseous states. | |||
* [[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). | |||
===Open systems=== | |||
In [[thermodynamic]] [[Open system (systems theory)|open systems]], matter 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 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: | |||
:<math> \mathrm{d}U = \mathrm{\delta}Q + \mathrm{d}U_{in} - \mathrm{d} U_{out} - \mathrm{\delta} W</math> | |||
where <math>U_{in}</math> is the average internal energy entering the system and <math>U_{out}</math> is the average internal energy leaving the system. | |||
[[Image:First law open system.svg|250px|thumb|right|Fig.1 During [[Steady-state (chemical engineering)|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]] | |||
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. 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 ''pV work''), and ''shaft work'', which may be performed on some mechanical device. | |||
These two types of work are expressed in the equation: | |||
: <math>\mathrm{\delta}W = \mathrm{d}(p_{out}V_{out}) - \mathrm{d}(p_{in}V_{in}) + \mathrm{\delta}W_{shaft}</math> | |||
Substitution into the equation above for the control volume cv yields: | |||
: <math>\mathrm{d}U_{cv} = \mathrm{\delta}Q + \mathrm{d}U_{in} + \mathrm{d}(p_{in}V_{in}) - \mathrm{d}U_{out} - \mathrm{d}(p_{out}V_{out}) - \mathrm{\delta}W_{shaft}</math>. | |||
The definition of enthalpy, <math>H</math>, permits us to use this [[thermodynamic potential]] to account for both internal energy and <math>pV</math> work in fluids for open systems: | |||
: <math>\mathrm{d}U_{cv} = \mathrm{\delta}Q + \mathrm{d}H_{in} - \mathrm{d}H_{out} - \mathrm{\delta}W_{shaft}</math>. | |||
This expression is described by Fig.1. 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.<ref>M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.129.</ref> In terms of time derivatives it reads | |||
: <math>\frac{\mathrm{d}U}{\mathrm{d}t} = \Sigma_k \dot Q_k + \Sigma_k \dot H_k - \Sigma_k p_k\frac{\mathrm{d}V_k}{\mathrm{d}t}-P,</math> | |||
where <math>\Sigma</math> represent algebraic sums and the indices ''k'' refer to the various places where heat is supplied, matter flows into the system, and boundaries are moving. The <math>\dot H_k</math> terms represent enthalpy flows, which can be written as | |||
:<math>\dot H_k = h_k\dot m_k = H_m\dot n_k</math> | |||
with <math>\dot m_k</math> the mass flow and <math>\dot n_k</math> the molar flow at position ''k'' respectively. The term d''V''<sub>k</sub>/d''t'' 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 e.g. 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. Otherwise, it has to be included in the enthalpy balance. During [[Steady-state (chemical engineering)|steady-state]] operation of a device (''see [[turbine]], [[pump]], and [[engine]]''), the average d''U''/d''t'' may be set equal to zero. This yields a useful expression for the average [[Power (physics)|power]] generation for these devices in the absence of chemical reactions | |||
:<math> P = \Sigma_k \left\langle \dot Q_k \right\rangle | |||
+ \Sigma_k \left\langle \dot H_k \right\rangle | |||
- \Sigma_k \left\langle p_k\frac{\mathrm{d}V_k}{\mathrm{d}t} \right\rangle</math> | |||
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. | |||
[[File:Ts diagram of N2 02.jpg|500px|thumb|right|Fig.2 Ts diagram of nitrogen. The red curve at the left is the melting curve. The red dome represents the two-phase region with the low-entropy side the saturated liquid and the high-entropy side the saturated gas. The black curves give the Ts relation along isobars. The pressures are indicated in bar. The blue curves are isenthalps (curves of constant enthalpy). The values are indicated in blue in kJ/kg. The specific points a, b, etc., are treated in the main text.]] | |||
==Diagrams== | |||
Nowadays the enthalpy values of important substances can be obtained via 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 hT diagrams, which give the specific enthalpy as function of temperature for various pressures and hp diagrams, which give ''h'' as function of ''p'' for various ''T''. One of the most common diagrams is the temperature-entropy diagram (Ts-diagram). An example is ''Fig.2'', which is the Ts-diagram of nitrogen.<ref>Figure composed with data obtained with RefProp, NIST Standard Reference Database 23</ref> 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. | |||
[[File:Schematic of throttling and compressor 01.jpg|400px|thumb|right|Fig.3 Two open systems in the steady state. Fluid enters the system (dotted rectangle) at point 1 and leaves it at point 2. The mass flow is <math>\dot m</math>. a: schematic diagram of the throttling process. b: schematic diagram of a compressor. A power ''P'' is applied and a heat flow <math>\dot Q</math> is released to the surroundings at ambient temperature ''T''<sub>a</sub>.]] | |||
==Some basic applications== | |||
The points a through h in Fig.2 play a role in the discussion in this Section. | |||
:a ''T'' = 300 K, ''p'' = 1 bar, ''s'' = 6.85 kJ/(kgK), ''h'' = 461 kJ/kg; | |||
:b ''T'' = 380 K, ''p'' = 2 bar, ''s'' = 6.85 kJ/(kgK), ''h'' = 530 kJ/kg; | |||
:c ''T'' = 300 K, ''p'' = 200 bar, ''s'' = 5.16 kJ/(kgK), ''h'' = 430 kJ/kg; | |||
:d ''T'' = 270 K, ''p'' = 1 bar, ''s'' = 6.79 kJ/(kgK), ''h'' = 430 kJ/kg; | |||
:e ''T'' = 108 K, ''p'' = 13 bar, ''s'' = 3.55 kJ/(kgK), ''h'' = 100 kJ/kg (saturated liquid at 13 bar); | |||
:f ''T'' = 77.2 K, ''p'' = 1 bar, ''s'' = 3.75 kJ/(kgK), ''h'' = 100 kJ/kg; | |||
:g ''T'' = 77.2 K, ''p'' = 1 bar, ''s'' = 2.83 kJ/(kgK), ''h'' = 28 kJ/kg (saturated liquid at 1 bar); | |||
:h ''T'' = 77.2 K, ''p'' = 1 bar, ''s'' = 5.41 kJ/(kgK), ''h'' =230 kJ/kg (saturated gas at 1 bar); | |||
===Throttling=== | |||
{{main|Joule–Thomson effect}} | |||
One of the simple applications of the concept of enthalpy is the so-called throttling process, also known as [[Joule–Thomson effect|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 Fig.3a. 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 fridge. It is also the final stage in many types of liquefiers. | |||
In the first law for open systems, applied to the system in Fig.3a, all terms are zero except the terms for the enthalpy flow. Hence | |||
:<math>0=\dot m h_1 - \dot m h_2.</math> | |||
Since the mass flow is constant the specific enthalpies at the two sides of the flow resistance are the same | |||
:<math>h_1 = h_2.</math> | |||
The consequences of this relation can be demonstrated using Fig.2. Point c in Fig.2 is at 200 bar and room temperature (300 K). A Joule-Thomson expansion from 200 to 1 bar follows a curve (not shown in Fig.2) in 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 one 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''<sub>f</sub>) is equal to the enthalpy in g (''h''<sub>g</sub>) multiplied with the liquid fraction in f (''x''<sub>f</sub>) plus the enthalpy in h (''h''<sub>h</sub>) multiplied with the gas fraction in f (1-''x''<sub>f</sub>). So | |||
:<math> h_f = x_f h_g+(1-x_f)h_h.</math> | |||
With numbers: 100 = ''x''<sub>f</sub> 28 + (1 - ''x''<sub>f</sub>)230 so ''x''<sub>f</sub> = 0.64. This means that the mass fraction of the liquid in the liquid-gas mixture that leaves the throttling valve is 64%. | |||
===Compressors=== | |||
{{main|Gas compressor}} | |||
Fig.3b is a schematic drawing of a compressor. 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 Fig.2. E.g. 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''<sub>a</sub> 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 <math>\dot Q</math>. Since the system is in the steady state the first law gives | |||
:<math>0=-\dot Q + \dot m h_1 - \dot m h_2 + P.</math> | |||
The minimum power, needed for the compression is realized if the compression is reversible. In that case the [[second law of thermodynamics]] for open systems gives | |||
:<math>0=-\frac{\dot Q}{T_a} + \dot m s_1 - \dot m s_2.</math> | |||
Eliminating <math>\dot Q</math> gives for the minimum power | |||
:<math>\frac{P_{\rm min}}{\dot m} = h_2-h_1 - T_a(s_2-s_1).</math> | |||
E.g. compressing 1 kg of nitrogen from 1 bar to 200 bar costs at least (''h''<sub>c</sub> - ''h''<sub>a</sub>) - ''T''<sub>a</sub>(''s''<sub>c</sub>-''s''<sub>a</sub>). With the data, obtained with Fig.2, 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 | |||
:<math>\frac{P_{\rm min}}{\dot m} = \int_1^2(\mathrm{d}h-T_a\mathrm{d}s).</math> | |||
With d''h'' = ''T''d''s'' + ''v''d''p'' this results in the final relation | |||
:<math>\frac{P_{\rm min}}{\dot m} = \int_1^2v\mathrm{d}p.</math> | |||
==See also== | |||
* [[Standard enthalpy change of formation (data table)]] | |||
* [[Calorimetry]] | |||
* [[Calorimeter]] | |||
* [[Departure function]] | |||
* [[Hess's law]] | |||
* [[Isenthalpic process]] | |||
* [[Stagnation enthalpy]] | |||
* [[Thermodynamic databases for pure substances]] | |||
==Notes== | |||
{{Reflist|group=note}} | |||
==References== | |||
{{Reflist}} | |||
==Bibliography== | |||
* 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''; S.R Furphy and Company, New York, 1980; p246 | |||
* DeHoff, R. ''Thermodynamics in Materials Science: 2nd ed.''; Taylor and Francis Group, New York, 2006. | |||
==External links== | |||
* [http://scienceworld.wolfram.com/physics/Enthalpy.html Enthalpy] - Eric Weisstein's World of Physics | |||
* [http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/firlaw.html Enthalpy] - Georgia State University | |||
* [http://www.chem.tamu.edu/class/majors/tutorialnotefiles/enthalpy.htm Enthalpy example calculations] - Texas A&M University Chemistry Department | |||
[[Category:State functions]] | |||
[[Category:Enthalpy| ]] | |||
[[Category:Energy (physics)]] | |||
[[Category:Physical quantities]] |
Revision as of 17:41, 26 January 2014
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Enthalpy is a measure of the total energy of a thermodynamic system. It includes the system's internal energy and thermodynamic potential (a state function), as well as its volume and pressure (the energy required to "make room for it" by displacing its environment, which is an extensive quantity). The unit of measurement for enthalpy in the International System of Units (SI) is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie.
The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer. Enthalpy change accounts for energy transferred to the environment at constant pressure through expansion or heating.
The total enthalpy, H, of a system cannot be measured directly. The same situation exists in classical mechanics: only a change or difference in energy carries physical meaning. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; therefore what we measure is the change in enthalpy, ΔH. The change ΔH is positive in endothermic reactions, and negative in heat-releasing exothermic processes. ΔH of a system is equal to the sum of non-mechanical work done on it and the heat supplied to it.
For processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.[1] This means that the change in enthalpy under such conditions is the heat absorbed (or released) by the material through a chemical reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume standard state: most commonly 1 bar pressure. Standard state does not, strictly speaking, specify a temperature (see standard state), but expressions for enthalpy generally reference the standard heat of formation at 25 °C.
Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy and Gibbs energy. Real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses.
Origins
The word enthalpy is based on the Greek noun enthalpos (ἔνθαλπος), which means heating. It comes from the Classical Greek prefix ἐν-, en-, meaning to put into, and the verb θάλπειν, thalpein, meaning "to heat". The word enthalpy is often incorrectly attributedPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. to Benoît Paul Émile Clapeyron and Rudolf Clausius through the 1850 publication of their Clausius-Clapeyron relation. This misconception was popularized by the 1927 publication of The Mollier Steam Tables and Diagrams. However, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyron's death.
The earliest writings to contain the concept of enthalpy did not appear until 1875,[2] when Josiah Willard Gibbs introduced "a heat function for constant pressure". However, Gibbs did not use the word "enthalpy" in his writings.[note 1] The actual word first appears in the scientific literature in a 1909 publication by J. P. Dalton. According to that publication, Heike Kamerlingh Onnes (1853-1926) actually coined the word.[3]
Over the years, many different symbols were used to denote enthalpy. It was not until 1922 that Alfred W. Porter proposed the symbol "H" as the accepted standard,[4] thus finalizing the terminology still in use today.
Formal definition
The enthalpy of a homogeneous system is defined as:[5][6]
where
- H is the enthalpy of the system
- U is the internal energy of the system
- p is the pressure of the system
- V is the volume of the system.
The enthalpy is an extensive property. This means that, for homogeneous systems, the enthalpy is proportional to the size of the system. It is convenient to introduce the specific enthalpy h =H/m where m is the mass of the system, or the molar enthalpy Hm = H/n, where n is the number of moles (h and Hm are intensive properties). For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems
where the label k refers to the various subsystems. In case of continuously varying p, T, and/or composition the summation becomes an integral:
where ρ is the density.
The enthalpy H(S,p) of homogeneous systems can be derived as a characteristic function of the entropy S and the pressure p as follows: we start from the first law of thermodynamics for closed systems for an infinitesimal process
Here, δQ is a small amount of heat added to the system and δW a small amount of work performed by the system. In a homogeneous system only reversible processes can take place so the second law of thermodynamics gives δQ = TdS with T the absolute temperature of the system. Furthermore, if only pV work is done, δW = pdV. As a result
Adding d(pV) to both sides of this expression gives
or
So
Other expressions
The expression of dH in terms of entropy and pressure may be unfamiliar to many readers. However, there are expressions in terms of more familiar variables such as temperature and pressure[7][8]
Here Cp 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 Cp and V are known as functions of p and T.
Notice that for an ideal gas, ,[note 2] so that:
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 μi is the chemical potential per particle for an i-type particle, and Ni is the number of such particles. The last term can also be written as μidni (with dni the number of moles of component i added to the system and, in this case, μi the molar chemical potential) or as μidmi (with dmi the mass of component i added to the system and, in this case, μi the specific chemical potential).
Enthalpy versus internal energy
The U term can be interpreted as the energy required to create the system, and the pV term as the energy 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 basic physics and statistical mechanics it may be more interesting to study the internal properties of the system and therefore the internal energy is used.[9][10] In basic chemistry, experiments are often conducted at atmospheric pressure and H is therefore more useful for reaction energy calculations. Furthermore the enthalpy is the workhorse of engineering thermodynamics as we will see later.
Relationship to heat
In order to discuss the relation between the enthalpy increase and heat supply we return to the first law for closed systems: dU = δQ - δW. We apply it to the special case that the pressure at the surface is uniform. In this case the work term can be split in two contributions, the so-called pV work, given by pdV (where here p is the pressure at the surface, dV is the increase of the volume of the system) and other types of work δW ' such as by a shaft or by electromagnetic interaction. So we write δW = pdV+δW '. In this case the first law reads
or
From this relation we see that the increase in enthalpy of a system is equal to the added heat
provided that the system is under constant pressure (dp = 0) and that the only work done by the system is expansion work (δW ' = 0)[11]
Applications
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 constancy of conditions present at the creation of the thermodynamic system.
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. This internal energy also includes the energy required for activation and the breaking of bonded compounds into gaseous species.
This process is calculated within enthalpy calculations as U + pV, 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.
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 pV is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.
Heat of reaction
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
is the final enthalpy of the system, expressed in joules. In a chemical reaction, is the enthalpy of the products.
is the initial enthalpy of the system, expressed in joules. In a chemical reaction, is the enthalpy of the reactants.
For an exothermic reaction at constant pressure, the system's change in enthalpy equals the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. 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. 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. However, few real-world applications exist in closed isolation, and it is for this reason that two or more closed systems cannot correctly be compared using enthalpy as a basis.
Specific enthalpy
As noted before, 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.
Enthalpy changes
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, and the initial enthalpy of the system, i.e. the reactants. These processes are reversible and the enthalpy for the reverse process is the negative value of the forward change.
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 temperature of 25 °C or 298 K,
- A pressure of one atmosphere (1 atm or 101.325 kPa),
- 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 atomize one mole of compound 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 between solid and liquid states.
- Enthalpy of vaporization, defined as the enthalpy change required to completely change the state of one mole of substance between liquid and gaseous states.
- Enthalpy of sublimation, defined as the enthalpy change required to completely change the state of one mole of substance between solid and gaseous states.
- 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).
Open systems
In thermodynamic open systems, matter 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 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:
where is the average internal energy entering the system and is the average internal energy leaving the system.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/First_law_open_system.svg/250px-First_law_open_system.svg.png)
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. 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 pV work), and shaft work, which may be performed on some mechanical device.
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, , permits us to use this thermodynamic potential to account for both internal energy and work in fluids for open systems:
This expression is described by Fig.1. 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.[12] In terms of time derivatives it reads
where represent algebraic sums and the indices k refer to the various places where heat is supplied, matter flows into the system, and boundaries are moving. The terms represent enthalpy flows, which can be written as
with the mass flow and the molar flow at position k respectively. The term dVk/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 e.g. 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. 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.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Ts_diagram_of_N2_02.jpg/500px-Ts_diagram_of_N2_02.jpg)
Diagrams
Nowadays the enthalpy values of important substances can be obtained via 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 hT diagrams, which give the specific enthalpy as function of temperature for various pressures and hp diagrams, which give h as function of p for various T. One of the most common diagrams is the temperature-entropy diagram (Ts-diagram). An example is Fig.2, which is the Ts-diagram of nitrogen.[13] 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.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Schematic_of_throttling_and_compressor_01.jpg/400px-Schematic_of_throttling_and_compressor_01.jpg)
Some basic applications
The points a through h in Fig.2 play a role in the discussion in this Section.
- a T = 300 K, p = 1 bar, s = 6.85 kJ/(kgK), h = 461 kJ/kg;
- b T = 380 K, p = 2 bar, s = 6.85 kJ/(kgK), h = 530 kJ/kg;
- c T = 300 K, p = 200 bar, s = 5.16 kJ/(kgK), h = 430 kJ/kg;
- d T = 270 K, p = 1 bar, s = 6.79 kJ/(kgK), h = 430 kJ/kg;
- e T = 108 K, p = 13 bar, s = 3.55 kJ/(kgK), h = 100 kJ/kg (saturated liquid at 13 bar);
- f T = 77.2 K, p = 1 bar, s = 3.75 kJ/(kgK), h = 100 kJ/kg;
- g T = 77.2 K, p = 1 bar, s = 2.83 kJ/(kgK), h = 28 kJ/kg (saturated liquid at 1 bar);
- h T = 77.2 K, p = 1 bar, s = 5.41 kJ/(kgK), h =230 kJ/kg (saturated gas at 1 bar);
Throttling
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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 Fig.3a. 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 fridge. It is also the final stage in many types of liquefiers.
In the first law for open systems, applied to the system in Fig.3a, all terms are zero except the terms for the enthalpy flow. Hence
Since the mass flow is constant the specific enthalpies at the two sides of the flow resistance are the same
The consequences of this relation can be demonstrated using Fig.2. Point c in Fig.2 is at 200 bar and room temperature (300 K). A Joule-Thomson expansion from 200 to 1 bar follows a curve (not shown in Fig.2) in 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 one 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 (hf) is equal to the enthalpy in g (hg) multiplied with the liquid fraction in f (xf) plus the enthalpy in h (hh) multiplied with the gas fraction in f (1-xf). So
With numbers: 100 = xf 28 + (1 - xf)230 so xf = 0.64. This means that the mass fraction of the liquid in the liquid-gas mixture that leaves the throttling valve is 64%.
Compressors
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Fig.3b is a schematic drawing of a compressor. 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 Fig.2. E.g. 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 Ta 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 . Since the system is in the steady state the first law gives
The minimum 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 gives for the minimum power
E.g. compressing 1 kg of nitrogen from 1 bar to 200 bar costs at least (hc - ha) - Ta(sc-sa). With the data, obtained with Fig.2, 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 = Tds + vdp this results in the final relation
See also
- Standard enthalpy change of formation (data table)
- Calorimetry
- Calorimeter
- Departure function
- Hess's law
- Isenthalpic process
- Stagnation enthalpy
- Thermodynamic databases for pure substances
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
Bibliography
- 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; S.R Furphy and Company, New York, 1980; p246
- DeHoff, R. Thermodynamics in Materials Science: 2nd ed.; Taylor and Francis Group, New York, 2006.
External links
- Enthalpy - Eric Weisstein's World of Physics
- Enthalpy - Georgia State University
- Enthalpy example calculations - Texas A&M University Chemistry Department
- ↑ G.J. Van Wylen and R.E. Sonntag (1985), Fundamentals of Classical Thermodynamics, Section 5.5 (3rd edition), John Wiley & Sons Inc. New York, NY. ISBN 0-471-82933-1
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ E.A. Guggenheim, Thermodynamics, North-Holland Publisching Company, Amsterdam, 1959
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Guggenheim, p. 88
- ↑ M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.511.
- ↑ F. Reif Statistical physics McGraw-Hill, London (1967)
- ↑ C. Kittel and H. Kroemer Thermal physics Freeman London (1980)
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.129.
- ↑ Figure composed with data obtained with RefProp, NIST Standard Reference Database 23
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