Enthalpy
From Free net encyclopedia
Template:Thermodynamic potentials
Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume and pressure. Etymology: enthalpy [1] is composed of the prefix en [2] [3] , plus the Greek verb thalpein, meaning to heat.
Enthalpy is a quantifiable state function, and the total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy is a thermodynamic potential, and is useful particularly for nearly-constant pressure processes, where any energy input to the system must go into internal energy or the mechanical work of expanding the system. The change in enthalpy of a system is nearly singularly meaningful for systems at constant pressure, when the change in enthalpy is equivalent to heat. Otherwise, there is no easily-interpreted meaning for this state function. as heat of the reaction for reactions performed at constant pressure. 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.
Enthalpy is defined by the following equation:
- <math>H = U + PV \,</math>
where (all units given in SI)
- H is the enthalpy
- U is the internal energy, (joule)
- P is the pressure of the system, (pascal)
- V is the volume, (cubic metre)
Contents |
Some useful relationships
From the first law of thermodynamics:
- <math>dU = \delta Q - \delta W\,</math>
And differentiating the expression for H we have:
- <math>dH = dU + (PdV+VdP) \!</math>
<math>= \delta Q - PdV + PdV+VdP = \delta Q +VdP = TdS + VdP \!</math>
where
|
|
For a process that is not reversible, the second law of thermodynamics states that the increase in heat <math>\delta Q</math> is less than or equal to the product <math>TdS</math> of temperature <math>T</math> and the increase in entropy <math>dS</math>; thus
- <math>dH = \delta Q + VdP \le TdS+VdP\,</math>
It is seen that, if a thermodynamic process is isobaric (i.e., occurs at constant pressure), then dP = 0 and thus
- <math>dH = \delta Q \le TdS \,</math>
The difference in enthalpy is the maximum thermal energy attainable from the system in an isobaric process. This explains why it is sometimes called the heat content. That is, the integral of dH over any isobar in state space is the maximum thermal energy attainable from the system.
If, in addition, the entropy is held constant as well, i.e., <math>dS = 0</math>, the above equation becomes:
- <math>dH \le 0\,</math>
with the equality holding at equilibrium. It is seen that the enthalpy for a general system will continuously decrease to its minimum value, which it maintains at equilbrium.
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 is then:
- <math>dH = \delta Q + VdP + \sum_i \mu_i dN_i \le TdS+VdP + \sum_i \mu_i dN_i\,</math>
where <math>\mu_i</math> is the chemical potential for an i-type particle, and <math>N_i</math> is the number of such particles. It is seen that, not only must the Vdp term be set to zero by requiring the pressures of the initial and final states to be the same, but the <math>\mu_i dN_i</math> terms must be zero as well, by requiring that the particle numbers remain unchanged. Any further generalization will add even more terms whose extensive differential term must be set to zero in order for the interpretation of the enthalpy to hold.
Applications
Heats 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:
- <math>\Delta H = H_{final} - H_{initial} \,</math>
where
- ΔH is the enthalpy change
- Hfinal is the final enthalpy of the system, measured in joules. In a chemical reaction, Hfinal is the enthalpy of the products.
- Hinitial is the initial enthalpy of the system, measured in joules. In a chemical reaction, Hinitial is the enthalpy of the reactants.
For an exothermic reaction at constant pressure, the system's change in enthalpy is equal to the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. 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 enthlapy than the reactants. The product of an endothermic reaction will be cold to the touch. 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. The product of an exothermic reaction will be warm to the touch.
Although Enthalpy is commonly used in engineering and science, being impossible to measure directly, 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 two or more closed systems cannot be compared using enthalpy as a basis, although it is sometimes erroneously.
Open systems
Image:First law open system.jpg
Open systems provide additional possibilities for performing work—by rotating a steam turbine for example. This "shaft work" is separate from work done on the fluid itself (called PV work):
- <math> \delta W = dW_{PV} + \delta W_{shaft} = d(PV) + \delta W_{shaft}\, </math>
The incorporation of the PV term into enthalpy is very useful for these systems. From the first law:
- <math>\frac{dU}{dt} = \frac{\delta Q}{dt} - \frac{d(PV)}{dt} - \frac{\delta W_{shaft}}{dt}\,</math>
and the definition of enthalpy:
- <math>dH = dU + d(PV)\,</math>
we obtain a version of the first law for shaft work in open systems with no chemical reaction:
- <math>\frac{dH}{dt} = \frac{\delta Q}{dt} - \frac{\delta W_{shaft}}{dt}\,</math>
This expression, like the first law expressed in terms of U, is not limited to reversible processes or any assumptions about the thermodynamic path taken by the process.
Standard enthalpy
The standard enthalpy change of reaction (denoted H° or Ho) is the enthalpy change that occurs in a system when 1 equivalent of matter is transformed by a chemical reaction under standard conditions.
A common standard enthalpy change is the standard enthalpy change of formation, which has been determined for a vast number of substances. The enthalpy change of any reaction under any conditions can be computed, given the standard enthalpy change of formation of all of the reactants and products. Other reactions with standard enthalpy change values include combustion (standard enthalpy change of combustion) and neutralisation (standard enthalpy change of neutralisation).
Specific enthalpy
The specific enthalpy of a working mass is a property of that mass used in thermodynamics, defined as <math>h=u+P*v</math> where u is the specific internal energy, P is the pressure, and v is specific volume. The SI unit for specific enthalpy is joules/kilogram.
See also
cs:Entalpie de:Enthalpie es:Entalpía fr:Enthalpie ko:엔탈피 it:Entalpia mk:Енталпија nl:Enthalpie ja:エンタルピー pl:Entalpia pt:Entalpia ru:Энтальпия sl:Entalpija fi:Entalpia sv:Entalpi zh:焓