Enthalpy

The enthalpy (of the prefix in and the Greek thalpein : to heat) is a Fonction of state of the Thermodynamique, whose variation makes it possible to express the quantity of Chaleur concerned during the transformation Isobare of a thermodynamic Système during which this one receives or provides a mechanical work.

Definition

Let us consider a transformation Monobare during which the system passes from a state has in a state B of balances by exchanging heat $Q\_p\; \backslash ;$ and of the work only via the compressive forces $W\_\; \{F,\; p\}\; \backslash ;$.

The First principle makes it possible to write:

$\backslash \; Delta\; U\; =\; U\_B\; -\; U\_A\; =\; Q\_p\; +\; W\_\; \{F,\; p\}\; \backslash ;$

U being the function of state energy interns

With constant pressure the work of the compressive forces is equal to:

$W\_\; \{F,\; p\}\; =\; -\; p\; \backslash \; Delta\; V\; =\; -\; p\; (V\_B\; -\; V\_A)\; \backslash ;$

$U\_B\; -\; U\_A\; =\; Q\_p\; -\; p\; (V\_B\; -\; V\_A)\; \backslash ;$

From where:

$Q\_p\; =\; (U\_B\; +\; pV\_B)\; -\; (U\_A\; +\; pV\_A)\; \backslash ;$

One thus defines a new function of state, the function enthalpy $H\; (U,\; p,\; V)\; \backslash ;$

It follows that:

$Q\_p\; =\; H\_B\; -\; H\_A\; =\; \backslash \; Delta\; H\; \backslash ;$

Consequently, with constant pressure, the heat concerned, which is not a function of state, becomes equal to the variation of the function of state enthalpy H. the variation of this function depends only on the final state and the initial state of the system and is independent of the way followed by the transformation.

It is the interest of the application of the function enthalpy in the very current cases of transformations carried out to the free air, with constant atmospheric pressure.

This property is at the base of the Calorimétrie to constant pressure. By abuse language one often confuses the terms heat and enthalpy.

Properties

The enthalpy with the dimension of a energy, and is expressed in joule S in the International system.

The induced mathematical property for any function of state implies that its Différentielle is total exact i.e. it is equal to the sum of the partial differentials compared to each variable.

Differential of the enthalpy

$H\; =\; U\; +\; statement\; \backslash ;$

$dH\; =\; of\; +\; pdV\; +\; Vdp\; \backslash ;$

• Let us apply the First principle

$of\; =\; \backslash \; delta\; Q\; -\; pdV\; \backslash ;$

$dH\; =\; \backslash \; delta\; Q\; -\; pdV\; +\; pdV\; +\; Vdp\; \backslash \; =\; \backslash \; delta\; Q\; +\; Vdp\; \backslash ;$

• Let us apply the second principle

$\backslash \; delta\; Q\; =\; TdS\; \backslash ;$ if the transformation is Réversible.

from where

$dH\; =\; TdS\; +\; Vdp\; \backslash ;$

Standard state

Standard state (standard conditions): state of reference for reagents and products: pure substance with P⁰ = 1 bar; T = cte; C⁰ = 1 mol. L-1 for an aqueous solution.

Standard state of reference: the most stable physical status with P⁰ = 1 bar and T = cte

Isenthalpic reaction

A isenthalpic reaction is a reaction where the enthalpy does not vary. An good example is the relaxation of Joule-Thomson.

See too

• free Enthalpy
• standard Enthalpy of formation
• Thermochemistry
• Specific heat
• Diagram of enthalpy
• Enthalpy of vaporization
• Entropy
• Perfect gas
• Law of Joule
• Temperature
• Function of state, variable of state, equation of state
• differential Calorimetry with sweeping

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