Specific EnthalpyEdit
Specific enthalpy is a fundamental property used to quantify the energy content per unit mass of a substance in a given state. In engineering practice, it provides a convenient way to account for energy transfers in flowing and non-flowing systems alike. The quantity is defined as h = u + p v, where h is the specific enthalpy, u is the specific internal energy, p is pressure, and v is the specific volume (the reciprocal of density). Because it is a state function, h depends only on the current state of the system, not on how that state was reached. This makes it especially useful in a wide range of applications from power generation to heating, ventilation, and air conditioning, and even in chemical processing where energy balances are essential. For most fluids, you will encounter enthalpy treated alongside thermodynamics as a core energy concept, and often with reference to a standard state or reference enthalpy for comparisons across conditions.
In many analyses, especially those involving flowing fluids, the concept of specific enthalpy simplifies the energy balance by absorbing the p v work term into a single property. When a fluid element is scaled by mass, the energy balance for a control volume or a moving fluid stream can be written in terms of h rather than u and p v separately, which is why you will see the steady-flow energy equation expressed with changes in h. This approach is widely used in engineering disciplines such as turbomachinery, steam turbines, and heat exchangers.
Definition and basic relations
Specific enthalpy is defined as h = u + p v, where:
- h = specific enthalpy (J/kg)
- u = specific internal energy (J/kg)
- p = pressure (Pa)
- v = specific volume (m^3/kg)
For a differential change in state, the fundamental relation gives dh = T ds + v dp, where T is temperature and s is specific entropy. This identity underpins how enthalpy changes respond to changes in temperature, pressure, and entropy.
At constant pressure, the differential simplifies to dh = c_p dT, where c_p is the specific heat capacity at constant pressure (often written as specific heat capacity). This makes h a convenient function of temperature for many liquids and gases under practical conditions.
For an ideal gas, h is a function of temperature only (h = h(T)), because p v = R T for an ideal gas, and the dependence on pressure collapses into the temperature dependence of the heat capacity. In this case, dh = c_p dT remains valid, and the enthalpy change between two states is obtained by integrating c_p over the temperature interval. See the notion of ideal gas for the governing simplifications.
For incompressible or nearly incompressible substances (typical of many liquids), h is also often approximated as a function of temperature alone, with dh ≈ c_p dT over modest temperature ranges. The precise behavior, of course, depends on the fluid's properties and phase behavior.
The relationship h = u + p v connects to other thermodynamic quantities:
- Since v = 1/ρ (ρ being density), h can also be written as h = u + p/ρ.
- The difference between enthalpy and internal energy, p v, represents the energy required to make room for the fluid at a given pressure—an accounting term that is especially relevant in flowing systems.
Enthalpy is a state function, like thermodynamics in a broader sense, and as such is typically tabulated for common fluids as a function of temperature and pressure. Data for h come from sources such as steam tables and modern equation-of-state libraries, and are often used in conjunction with standard enthalpy of formation when chemical reactions are involved.
Physical interpretation and state utilities
Enthalpy encapsulates both the internal energy of the molecules and the energy associated with their expansion at a given pressure. In a flowing system, it conveniently combines microscopic energy with the macroscopic work associated with volume changes, streamlining energy accounting in devices like pumps, compressors, and turbines.
In many practical calculations, especially in heating and cooling processes, engineers use h to compare the energy content of streams before and after processing. For moist air, for example, the concept extends to an enthalpy that includes latent heat effects due to water vapor content, and is used in HVAC design and meteorological analyses.
The standard enthalpy of formation and related data sets are essential when reacting systems are involved, because the enthalpy change of a reaction at a given temperature is often expressed as the difference between the enthalpies of products and reactants relative to chosen reference states. See standard enthalpy of formation for more on how reaction enthalpies are tabulated and used.
Applications and examples
Energy balances in closed and open systems: The steady-flow energy equation and its variants frequently rely on changes in h to quantify the energy carried by fluids across system boundaries. This is central to the design and analysis of heat exchangers, boilers, and energy recovery devices.
Power generation and propulsion: Turbomachines, steam cycles, and jet propulsion systems use specific enthalpy to track energy conversion and losses through successive components (compressors, turbines, nozzles). In these contexts, enthalpy changes relate directly to performance metrics like efficiency and work output.
Chemical engineering processes: In reacting and non-reacting processes, h is used alongside cp and cv to model heating/cooling duties, feed preheating, and product cooling. The enthalpy of reaction, derived from enthalpies of formation, is a central quantity in process design and safety analysis.
Moist air and HVAC design: For air–water-vapor mixtures, the enthalpy of moist air combines sensible and latent components, and is a key variable in comfort calculations and energy-intensive climate control systems. See moist air for a related treatment of the topic.
Calculation and data sources
Practical determination of h relies on thermodynamic data for the fluid, typically in the form of cp(T) data and equation-of-state formulations. For ideal gases or near-ideal conditions, enthalpy changes are computed by integrating c_p(T) with respect to temperature.
For many standard fluids, engineers consult tabulated data from steam tables or modern data libraries, which provide h as a function of T and p across a wide range of conditions. When dealing with mixtures, saturated phases, or high pressures, appropriate equations of state and mixture models are used to interpolate or extrapolate h accurately.
The choice of reference state matters: enthalpy is often reported relative to a baseline such as h = 0 at a reference temperature and pressure for a given substance, with standard references typically defined for a conventional environment. This practice lets practitioners compare enthalpy changes across processes without being distracted by absolute values.