Which Characteristic Describes The Troposphere

Measure of energy in a thermodynamic system

Enthalpy , a property of a thermodynamic organisation, is the sum of the organisation'due south internal energy and the product of its pressure and volume.^[1] Information technology is a country function used in many measurements in chemical, biological, and physical systems at a abiding pressure, which is conveniently provided by the big ambience atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its environs.^[two] ^[iii] The force per unit area-volume term is very small-scale for solids and liquids at common conditions, and fairly pocket-size for gases. Therefore, enthalpy is a stand up-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state part, enthalpy depends merely on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve information technology.

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

The total enthalpy of a system cannot be measured directly because the internal energy contains components that are unknown, non easily attainable, or are not of involvement in thermodynamics. In practice, a change in enthalpy is the preferred expression for measurements at constant force per unit area considering it simplifies the clarification of energy transfer. When transfer of thing into or out of the system is also prevented and no electrical or shaft work is done, at constant pressure the enthalpy change equals the free energy exchanged with the environment past rut.

In chemistry, the standard enthalpy of reaction is the enthalpy modify when reactants in their standard states ( $p$ = 1 bar; usually $T$ = 298 K) change to products in their standard states.^[iv] This quantity is the standard estrus of reaction at abiding force per unit area and temperature, just information technology tin be measured past calorimetric methods even if the temperature does vary during the measurement, provided that the initial and final pressure and temperature stand for to the standard state. The value does not depend on the path from initial to final state considering enthalpy is a land function.

Enthalpies of chemical substances are usually listed for 1 bar (100 kPa) pressure as a standard country. Enthalpies and enthalpy changes for reactions vary every bit a part of temperature,^[five] simply tables generally list the standard heats of formation of substances at 25 °C (298 K). For endothermic (heat-arresting) processes, the change $Δ H$ is a positive value; for exothermic (heat-releasing) processes it is negative.

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

Definition [edit]

The enthalpy $H$ of a thermodynamic system is defined as the sum of its internal energy and the production of its pressure level and book:^[one]

H = U + pV

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

Enthalpy is an all-encompassing belongings; it is proportional to the size of the system (for homogeneous systems). As intensive properties, the specific enthalpy $h = H / m$ is referenced to a unit of measurement of mass $thou$ of the system, and the molar enthalpy $H m is H / n$ , where $n$ is the number of moles. For inhomogeneous systems the enthalpy is the sum of the enthalpies of the component subsystems:

H=\sum _{k}H_{thou},

where

$H$ is the full enthalpy of all the subsystems,
$m$ refers to the various subsystems,
$H k$ refers to the enthalpy of each subsystem.

A airtight system may prevarication in thermodynamic equilibrium in a static gravitational field, so that its force per unit area $p$ varies continuously with altitude, while, because of the equilibrium requirement, its temperature $T$ is invariant with altitude. (Correspondingly, the organization's gravitational potential free energy density besides varies with altitude.) Then the enthalpy summation becomes an integral:

H=\int (\rho h)\,dV,

where

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

The enthalpy of a airtight homogeneous arrangement is its energy function $H (S, p)$ , with its entropy $S [p]$ and its pressure $p$ every bit natural land variables which provide a differential relation for dH of the simplest form, derived as follows. We start from the first law of thermodynamics for closed systems for an minute procedure:

dU=\delta Q-\delta W,

where

$𝛿 Q$ is a pocket-size corporeality of heat added to the system,
$𝛿 W$ is a small amount of piece of work performed by the system.

In a homogeneous system in which simply reversible processes or pure heat transfer are considered, the second police force of thermodynamics gives $𝛿 Q = T dS$ , with $T$ the accented temperature and $dS$ the infinitesimal change in entropy $S$ of the arrangement. Furthermore, if simply $pV$ work is done, $𝛿 W = p dV$ . Every bit a outcome,

dU=T\,dS-p\,dV.

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

dU+d(pV)=T\,dS-p\,dV+d(pV),

d(U+pV)=T\,dS+5\,dp.

And then

dH(Due south,p)=T\,dS+V\,dp.

and the coefficients of the natural variable differentials dS and dp are just the single variables T and Five.

Other expressions [edit]

The above expression of $dH$ in terms of entropy and force per unit area may be unfamiliar to some readers. There are besides expressions in terms of more directly measurable variables such every bit temperature and pressure level:^{[half dozen]} ^: 88 ^[7]

dH=C_{p}\,dT+V(1-\alpha T)\,dp.

Here $C p$ is the oestrus capacity at constant pressure and $α$ is the coefficient of (cubic) thermal expansion:

\alpha ={\frac {1}{Five}}\left({\frac {\fractional V}{\fractional T}}\right)_{p}.

With this expression one can, in principle, determine the enthalpy if $C p$ and $V$ are known as functions of $p$ and $T$ . However the expression is more complicated than $dH=T\,dS+V\,dp$ because T is not a natural variable for the enthalpy H.

At constant pressure, dP = 0 and then that $dH=C_{p}\,dT.$ For an platonic gas, dH reduces to this form even if the process involves a force per unit area change, because $αT = 1$ ,^{[notation i]}.

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

dH=T\,dS+Five\,dp+\sum _{i}\mu _{i}\,dN_{i},

where $μ i$ is the chemical potential per particle for an $i$ -blazon particle, and $N i$ is the number of such particles. The last term tin likewise exist written equally $μ i dn i$ (with $dn i$ the number of moles of component $i$ added to the system and, in this case, $μ i$ the tooth chemic potential) or as $μ i dm i$ (with $dm i$ the mass of component $i$ added to the organization and, in this case, $μ i$ the specific chemic potential).

Characteristic functions and natural state variables [edit]

The enthalpy, $H (S [p], p, {Northward i})$ , expresses the thermodynamics of a organization in the energy representation. As a function of land, its arguments include both one intensive and several extensive state variables. The state variables $Due south [p]$ , $p$ , and ${Northward i}$ are said to be the natural state variables in this representation. They are suitable for describing processes in which they are determined by factors in the environs. For case, when a virtual package of atmospheric air moves to a dissimilar altitude, the pressure surrounding it changes, and the process is often so rapid that there is also little time for heat transfer. This is the basis of the then-called adiabatic approximation that is used in meteorology.^[8]

Conjugate with the enthalpy, with these arguments, the other characteristic function of state of a thermodynamic system is its entropy, as a function, $S [p](H, p, {N i})$ , of the same listing of variables of state, except that the entropy, $Due south [p]$ , is replaced in the list past the enthalpy, $H$ . It expresses the entropy representation. The state variables $H$ , $p$ , and ${N i}$ are said to be the natural state variables in this representation. They are suitable for describing processes in which they are experimentally controlled. For instance, $H$ and $p$ can be controlled by allowing rut transfer, and by varying only the external pressure on the piston that sets the book of the system.^[ix] ^[10] ^[11]

Physical estimation [edit]

The $U$ term is the free energy of the system, and the $pV$ term can be interpreted as the work that would exist required to "make room" for the organization if the pressure of the environment remained abiding. When a system, for example, $northward$ moles of a gas of volume $V$ at pressure $p$ and temperature $T$ , is created or brought to its present state from absolute cypher, energy must exist supplied equal to its internal free energy $U$ plus $pV$ , where $pV$ is the piece of work done in pushing confronting the ambient (atmospheric) force per unit area.

In physics and statistical mechanics it may be more interesting to study the internal properties of a constant-book system and therefore the internal energy is used.^[12] ^[thirteen] In chemical science, experiments are often conducted at constant atmospheric pressure, and the pressure–book piece of work represents a small, well-defined free energy exchange with the atmosphere, then that $Δ H$ is the advisable expression for the heat of reaction. For a heat engine, the change in its enthalpy later a total cycle is equal to zero, since the concluding and initial state are equal.

Relationship to heat [edit]

In order to talk over the relation between the enthalpy increase and heat supply, we render to the first law for airtight systems, with the physics sign convention: $dU = δQ - δW$ , where the heat $δQ$ is supplied past conduction, radiation, Joule heating. Nosotros apply it to the special instance with a constant force per unit area at the surface. In this case the work is given by $p dV$ (where $p$ is the pressure at the surface, $dV$ is the increase of the volume of the arrangement). Cases of long range electromagnetic interaction require further country variables in their formulation, and are not considered here. In this case the first law reads:

dU=\delta Q-p\,dV.

At present,

dH=dU+d(pV).

{\begin{aligned}dH&=\delta Q+V\,dp+p\,dV-p\,dV\\&=\delta Q+V\,dp.\end{aligned}}

If the arrangement is nether constant pressure, $dp = 0$ and consequently, the increase in enthalpy of the organization is equal to the heat added:

dH=\delta Q.

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

Applications [edit]

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

Free energy must be supplied to remove particles from the environment to brand space for the creation of the system, assuming that the pressure level $p$ remains constant; this is the $pV$ term. The supplied energy must as well provide the change in internal energy, $U$ , which includes activation energies, ionization energies, mixing energies, vaporization energies, chemic bond energies, and and then forth. Together, these establish the modify in the enthalpy $U + pV$ . For systems at constant pressure, with no external work washed other than the $pV$ piece of work, the change in enthalpy is the heat received past the organization.

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

Oestrus of reaction [edit]

The full enthalpy of a organisation cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy modify is defined past the post-obit equation:

\Delta H=H_{\mathrm {f} }-H_{\mathrm {i} },

where

$Δ H$ is the "enthalpy change",
$H f$ is the final enthalpy of the system (in a chemical reaction, the enthalpy of the products or the system at equilibrium),
$H i$ is the initial enthalpy of the arrangement (in a chemic reaction, the enthalpy of the reactants).

For an exothermic reaction at constant force per unit area, the system's change in enthalpy, $Δ H$ , is negative due to the products of the reaction having a smaller enthalpy than the reactants, and equals the heat released in the reaction if no electric or shaft work is washed. In other words, the overall decrease in enthalpy is achieved by the generation of oestrus.^[fifteen] Conversely, for a abiding-force per unit area endothermic reaction, $Δ H$ is positive and equal to the oestrus absorbed in the reaction.

From the definition of enthalpy as $H = U + pV$ , the enthalpy change at constant force per unit area is $Δ H = Δ U + p Δ Five$ . Withal for most chemical reactions, the work term $p Δ V$ is much smaller than the internal energy change $Δ U$ , which is approximately equal to $Δ H$ . As an example, for the combustion of carbon monoxide 2 CO(g) + O₂(thou) → two CO_ii(g), $Δ H = -566.0 kJ$ and $Δ U = -563.5 kJ$ .^[16] Since the differences are so modest, reaction enthalpies are frequently described as reaction energies and analyzed in terms of bond energies.

Specific enthalpy [edit]

The specific enthalpy of a uniform system is defined as $h = H / 1000$ where $m$ is the mass of the system. The SI unit for specific enthalpy is joule per kilogram. It tin can be expressed in other specific quantities past $h = u + pv$ , where $u$ is the specific internal energy, $p$ is the pressure level, and $v$ is specific volume, which is equal to $i / ρ$ , where $ρ$ is the density.

Enthalpy changes [edit]

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

A mutual standard enthalpy modify is the enthalpy of formation, which has been determined for a big 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 pick of enthalpy changes normally recognized in thermodynamics.

When used in these recognized terms the qualifier alter is ordinarily dropped and the belongings is simply termed enthalpy of 'procedure'. Since these properties are frequently used as reference values it is very mutual to quote them for a standardized set of environmental parameters, or standard conditions, including:

A force per unit area of one atmosphere (1 atm or 101.325 kPa) or 1 bar
A temperature of 25 °C or 298.15 M
A concentration of 1.0 Grand when the element or compound is present in solution
Elements or compounds in their normal concrete states, i.due east. standard land

For such standardized values the proper noun of the enthalpy is commonly prefixed with the term standard, e.g. standard enthalpy of germination.

Chemical properties:

Enthalpy of reaction, defined as the enthalpy alter observed in a elective of a thermodynamic system when one mole of substance reacts completely.
Enthalpy of germination, defined as the enthalpy modify observed in a constituent of a thermodynamic organisation when i mole of a compound is formed from its elementary antecedents.
Enthalpy of combustion, defined every bit the enthalpy change observed in a elective of a thermodynamic system when 1 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 i mole of an unsaturated compound reacts completely with an excess of hydrogen to class a saturated compound.
Enthalpy of atomization, divers as the enthalpy modify required to separate i mole of a substance into its constituent atoms completely.
Enthalpy of neutralization, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of h2o is formed when an acid and a base react.
Standard Enthalpy of solution, defined as the enthalpy alter observed in a elective of a thermodynamic system when one mole of a solute is dissolved completely in an excess of solvent, so that the solution is at space dilution.
Standard enthalpy of Denaturation (biochemistry), defined as the enthalpy modify required to denature one mole of compound.
Enthalpy of hydration, defined as the enthalpy modify observed when one mole of gaseous ions are completely dissolved in water forming ane mole of aqueous ions.

Physical properties:

Enthalpy of fusion, divers every bit the enthalpy change required to completely change the state of 1 mole of substance from solid to liquid.
Enthalpy of vaporization, defined equally the enthalpy change required to completely modify the country of one mole of substance from liquid to gas.
Enthalpy of sublimation, divers as the enthalpy change required to completely modify the state of 1 mole of substance from solid to gas.
Lattice enthalpy, defined equally the energy required to separate 1 mole of an ionic compound into separated gaseous ions to an infinite altitude apart (meaning no strength of attraction).
Enthalpy of mixing, defined as the enthalpy modify upon mixing of two (non-reacting) chemical substances.

Open systems [edit]

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

dU=\delta Q+dU_{\text{in}}-dU_{\text{out}}-\delta W,

where $U in$ is the average internal free energy entering the system, and $U out$ is the average internal energy leaving the system.

During steady, continuous operation, an energy balance practical to an open system equates shaft work performed by the arrangement to rut added plus net enthalpy added

The region of space enclosed by the boundaries of the open organisation is commonly called a control volume, and it may or may not stand for to concrete walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the menstruation of mass into the organization performs work as if it were a piston of fluid pushing mass into the arrangement, and the arrangement performs work on the flow of mass out every bit if it were driving a piston of fluid. At that place are then two types of work performed: flow piece of work described to a higher place, which is performed on the fluid (this is too frequently called $pV$ piece of work), and shaft piece of work, which may be performed on some mechanical device such as a turbine or pump.

These two types of piece of work are expressed in the equation

\delta West=d(p_{\text{out}}V_{\text{out}})-d(p_{\text{in}}V_{\text{in}})+\delta W_{\text{shaft}}.

Substitution into the equation to a higher place for the control book (cv) yields:

dU_{\text{cv}}=\delta Q+dU_{\text{in}}+d(p_{\text{in}}V_{\text{in}})-dU_{\text{out}}-d(p_{\text{out}}V_{\text{out}})-\delta W_{\text{shaft}}.

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

dU_{\text{cv}}=\delta Q+dH_{\text{in}}-dH_{\text{out}}-\delta W_{\text{shaft}}.

If nosotros allow besides the system boundary to move (e.g. due to moving pistons), we go a rather full general form of the first law for open systems.^[17] In terms of fourth dimension derivatives it reads:

{\frac {dU}{dt}}=\sum _{thou}{\dot {Q}}_{one thousand}+\sum _{k}{\dot {H}}_{k}-\sum _{k}p_{k}{\frac {dV_{m}}{dt}}-P,

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

{\dot {H}}_{grand}=h_{k}{\dot {m}}_{k}=H_{\mathrm {m} }{\dot {n}}_{m},

with $ṁ chiliad$ the mass flow and $ṅ m$ the molar flow at position $k$ respectively. The term $dV k / dt$ represents the rate of modify of the organization volume at position $k$ that results in $pV$ power done past the system. The parameter $P$ represents all other forms of ability done by the organization such as shaft power, just it can too be, say, electric power produced past an electrical power institute.

Note that the previous expression holds true just if the kinetic energy menstruum charge per unit is conserved between arrangement inlet and outlet.^{[ clarification needed ]} Otherwise, information technology has to be included in the enthalpy remainder. 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 boilerplate ability generation for these devices in the absenteeism of chemical reactions:

P=\sum _{k}\left\langle {\dot {Q}}_{k}\correct\rangle +\sum _{k}\left\langle {\dot {H}}_{k}\right\rangle -\sum _{k}\left\langle p_{grand}{\frac {dV_{k}}{dt}}\right\rangle ,

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

Diagrams [edit]

$T - s$ diagram of nitrogen.^[18] The red curve at the left is the melting curve. The red dome represents the ii-stage region with the low-entropy side the saturated liquid and the high-entropy side the saturated gas. The black curves requite the $T - s$ relation along isobars. The pressures are indicated in bar. The blueish curves are isenthalps (curves of abiding enthalpy). The values are indicated in bluish in kJ/kg. The specific points a, b, etc., are treated in the master text.

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

Some basic applications [edit]

The points a through h in the figure play a role in the give-and-take in this section.

Betoken	$T$ (K)	$p$ (bar)	$due south$ (kJ/(kg K))	$h$ (kJ/kg)
a	300	1	half-dozen.85	461
b	380	2	6.85	530
c	300	200	5.xvi	430
d	270	i	half-dozen.79	430
e	108	13	three.55	100
f	77.2	1	3.75	100
chiliad	77.2	i	ii.83	28
h	77.ii	ane	5.41	230

Points e and thousand are saturated liquids, and indicate h is a saturated gas.

Throttling [edit]

Schematic diagram of a throttling in the steady state. Fluid enters the organization (dotted rectangle) at betoken 1 and leaves it at point ii. The mass flow is $ṁ$ .

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

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

0={\dot {one thousand}}h_{1}-{\dot {m}}h_{2}.

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

h_{ane}=h_{2},

that is, the enthalpy per unit mass does not change during the throttling. The consequences of this relation can be demonstrated using the $T - southward$ diagram higher up. Signal c is at 200 bar and room temperature (300 G). A Joule–Thomson expansion from 200 bar to 1 bar follows a bend of abiding enthalpy of roughly 425 kJ/kg (not shown in the diagram) lying betwixt 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 Grand to 270 G. In the valve, in that location 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 then that it is on the saturated liquid line with $h$ = 100 kJ/kg. It corresponds roughly with $p$ = 13 bar and $T$ = 108 M. Throttling from this betoken to a pressure level of 1 bar ends in the ii-phase region (point f). This means that a mixture of gas and liquid leaves the throttling valve. Since the enthalpy is an extensive parameter, the enthalpy in f ( $h f$ ) is equal to the enthalpy in yard ( $h g$ ) multiplied by the liquid fraction in f ( $x f$ ) plus the enthalpy in h ( $h h$ ) multiplied by the gas fraction in f $(one - 10 f)$ . So

h_{\mathbf {f} }=x_{\mathbf {f} }h_{\mathbf {m} }+(1-x_{\mathbf {f} })h_{\mathbf {h} }.

With numbers: $100 = x f \times 28 + (i - x f) \times 230$ , then $x f$ = 0.64. This means that the mass fraction of the liquid in the liquid–gas mixture that leaves the throttling valve is 64%.

Compressors [edit]

Schematic diagram of a compressor in the steady land. Fluid enters the arrangement (dotted rectangle) at point ane and leaves it at bespeak ii. The mass flow is $ṁ$ . A power $P$ is practical and a rut catamenia $Q̇$ is released to the environs at ambient temperature $T a$ .

A power $P$ is applied e.chiliad. equally electrical power. If the compression is adiabatic, the gas temperature goes upwards. In the reversible example it would be at constant entropy, which corresponds with a vertical line in the $T - s$ diagram. For example, compressing nitrogen from 1 bar (point a) to ii bar (point b) would result in a temperature increase from 300 K to 380 K. In order to let the compressed gas get out at ambient temperature $T a$ , heat substitution, e.g. by cooling h2o, is necessary. In the ideal case the pinch is isothermal. The average heat catamenia to the surround is $Q̇$ . Since the system is in the steady state the kickoff law gives

0=-{\dot {Q}}+{\dot {m}}h_{1}-{\dot {k}}h_{2}+P.

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

0=-{\frac {\dot {Q}}{T_{\mathrm {a} }}}+{\dot {m}}s_{1}-{\dot {m}}s_{2}.

Eliminating $Q̇$ gives for the minimal power

{\frac {P_{\text{min}}}{\dot {m}}}=h_{2}-h_{1}-T_{\mathrm {a} }(s_{2}-s_{1}).

For example, compressing 1 kg of nitrogen from ane bar to 200 bar costs at least $(h c - h a) - T a (s c - southward a)$ . With the data, obtained with the $T - s$ diagram, we discover a value of (430 − 461) − 300 × (v.xvi − half-dozen.85) = 476 kJ/kg.

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

{\frac {P_{\text{min}}}{\dot {m}}}=\int _{1}^{2}(dh-T_{\mathrm {a} }\,ds).

With $dh = T ds + v dp$ , this results in the concluding relation

{\frac {P_{\text{min}}}{\dot {m}}}=\int _{1}^{two}v\,dp.

History and etymology [edit]

The term enthalpy was coined relatively belatedly in the history of thermodynamics, in the early 20th century. Energy was introduced in a modern sense by Thomas Young in 1802, while entropy was coined by Rudolf Clausius in 1865. Free energy uses the root of the Greek word ἔργον (ergon), pregnant "work", to limited the idea of chapters to perform piece of work. Entropy uses the Greek word τροπή (tropē) meaning transformation or turning. Enthalpy uses the root of the Greek word θάλπος (thalpos) "warmth, oestrus".^[19]

The term expresses the obsolete concept of heat content,^[20] every bit $dH$ refers to the amount of heat gained in a process at constant force per unit area only,^[21] but not in the general case when pressure is variable.^[22] Josiah Willard Gibbs used the term "a rut part for constant force per unit area" for clarity.^{[note 2]}

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

The term enthalpy get-go appeared in print in 1909.^[23] It is attributed to Heike Kamerlingh Onnes, who well-nigh probable introduced it orally the year earlier, at the first meeting of the Institute of Refrigeration in Paris.^[24] It gained currency only in the 1920s, notably with the Mollier Steam Tables and Diagrams, published in 1927.

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

Run into also [edit]

Standard enthalpy alter of formation (data table)
Calorimetry
Calorimeter
Divergence part
Hess's police
Isenthalpic process
Laws of thermodynamics
Stagnation enthalpy
Thermodynamic databases for pure substances

Notes [edit]

^ $\alpha T={\frac {T}{V}}\left({\frac {\fractional ({\frac {nRT}{P}})}{\fractional T}}\right)_{p}={\frac {nRT}{PV}}=i$
^ The Collected Works of J. Willard Gibbs, Vol. I do non comprise reference to the word enthalpy, but rather reference the "heat part for abiding pressure". Come across: Henderson, Douglas; Eyring, Henry; Jost, Wilhelm (1967). Concrete Chemistry: An Advanced Treatise. Bookish Press. p. 29.

References [edit]

^ ^a ^b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "enthalpy". doi:10.1351/goldbook.E02141
^ Zemansky, Marker W. (1968). "Chapter 11". Estrus and Thermodynamics (5th ed.). New York, NY: McGraw-Hill. p. 275.
^ Van Wylen, Thousand. J.; Sonntag, R. Eastward. (1985). "Department 5.5". Fundamentals of Classical Thermodynamics (3rd ed.). New York: John Wiley & Sons. ISBN978-0-471-82933-i.
^ Atkins, Peter; de Paula, Julio (2006). Atkins' Physical Chemical science (8th ed.). W.H.Freeman. p. 51. ISBN0-7167-8759-8.
^ Laidler, Keith J.; Meiser, John H. (1999). Physical Chemistry (3 ed.). Boston: Houghton Mifflin. p. 66. ISBN0-395-91848-0.
^ Guggenheim, E. A. (1959). Thermodynamics. Amsterdam: North-Holland Publishing Visitor.
^ Moran, M. J.; Shapiro, H. N. (2006). Fundamentals of Technology Thermodynamics (5th ed.). John Wiley & Sons. p. 511. ISBN9780470030370.
^ Iribarne, J.V., Godson, W.L. (1981). Atmospheric Thermodynamics, 2nd edition, Kluwer Bookish Publishers, Dordrecht, ISBN xc-277-1297-2, pp. 235–236.
^ Tschoegl, N.Due west. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, ISBN 0-444-50426-5, p. 17.
^ Callen, H. B. (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, ISBN 0-471-86256-8, Chapter 5.
^ Münster, A. (1970), Classical Thermodynamics, translated by E. South. Halberstadt, Wiley–Interscience, London, ISBN 0-471-62430-6, p. 6.
^ Reif, F. (1967). Statistical Physics. London: McGraw-Hill.
^ Kittel, C.; Kroemer, H. (1980). Thermal Physics. London: Freeman.
^ Rathakrishnan (2015). High Enthalpy Gas Dynamics. John Wiley and Sons Singapore Pte. Ltd. ISBN978-1118821893.
^ Laidler, Keith J.; Meiser, John H. (1982). Physical Chemistry. Benjamin/Cummings. p. 53. ISBN978-0-8053-5682-3.
^ Petrucci, Ralph H.; Harwood, William South.; Herring, F. Geoffrey (2002). General Chemistry (eighth ed.). Prentice Hall. pp. 237–238. ISBN978-0-thirteen-014329-7.
^ Moran, M. J.; Shapiro, H. Northward. (2006). Fundamentals of Applied science Thermodynamics (5th ed.). John Wiley & Sons. p. 129. ISBN9780470030370.
^ Effigy composed with data obtained with RefProp, NIST Standard Reference Database 23.
^ θάλπος in A Greek–English language Lexicon.
^ Howard (2002) quotes J. R. Partington in An Advanced Treatise on Physical Chemistry (1949) as saying that the office H was "usually called the heat content".
^ Tinoco, Ignacio Jr.; Sauer, Kenneth; Wang, James C. (1995). Physical Chemistry (3rd ed.). Prentice-Hall. p. 41. ISBN978-0-thirteen-186545-vii.
^ Laidler, Keith J.; Meiser, John H. (1982). Concrete Chemical science. Benjamin/Cummings. p. 53. ISBN978-0-8053-5682-3.
^ Dalton, J. P. (1909). "Researches on the Joule–Kelvin-upshot, especially at low temperatures. I. Calculations for hydrogen". Proceedings of the Section of Sciences (Koninklijke Akademie van Wetenschappen te Amsterdam [Majestic Academy of Sciences at Amsterdam]). xi (office ii): 863–873. Bibcode:1908KNAB...11..863D. ; see p. 864, footnote (1).
^
Come across:
- Laidler, Keith (1995). The World of Concrete Chemistry. Oxford Academy Printing. p. 110.
- Van Ness, Hendrick C. (2003). "H Is for Enthalpy". Journal of Chemical Instruction. 80 (6): 486. Bibcode:2003JChEd..lxxx..486V. doi:10.1021/ed080p486.1.
^ Porter, Alfred W. (1922). "The generation and utilisation of common cold. A general word". Transactions of the Faraday Lodge. 18: 139–143. doi:ten.1039/tf9221800139. ; run into p. 140.
^ Howard, Irmgard (2002). "H Is for Enthalpy, Thanks to Heike Kamerlingh Onnes and Alfred W. Porter". Journal of Chemic Education. 79 (6): 697. Bibcode:2002JChEd..79..697H. doi:ten.1021/ed079p697.

Bibliography [edit]

Dalton, J.P. (1909). "Researches on the Joule–Kelvin effect, especially at low temperatures. I. Calculations for hydrogen" (PDF). KNAW Proceedings. 11: 863–873. Bibcode:1908KNAB...11..863D.
Haase, R. (1971). Jost, West. (ed.). Physical Chemistry: An Advanced Treatise. New York: Academic. p. 29.
Gibbs, J. West. The Collected Works of J. Willard Gibbs, Vol. I (1948 ed.). New Haven, CT: Yale University Press. p. 88.
Howard, I. G. (2002). "H Is for Enthalpy, Cheers to Heike Kamerlingh Onnes and Alfred W. Porter". J. Chem. Educ. 79 (6): 697–698. Bibcode:2002JChEd..79..697H. doi:10.1021/ed079p697.
Laidler, K. (1995). The World of Physical Chemical science . Oxford: Oxford Academy Press. p. 110. ISBN978-0-19-855597-i.
Kittel, C.; Kroemer, H. (1980). Thermal Physics. New York: S. R. Furphy & Co. p. 246.
DeHoff, R. (2006). Thermodynamics in Materials Science. CRC Press. ISBN9780849340659.

External links [edit]

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