Enthalpy and Entropy of Water

Thermodynamic Property Definitions

Enthalpy and entropy are fundamental thermodynamic properties essential for HVAC system analysis, steam system design, refrigeration cycle calculations, and energy balance computations.

Enthalpy (h)

Enthalpy represents the total heat content of a substance per unit mass, combining internal energy and flow work:

h = u + Pv

Where:

• h = specific enthalpy (Btu/lbm or kJ/kg)
• u = specific internal energy (Btu/lbm or kJ/kg)
• P = absolute pressure (lbf/ft² or Pa)
• v = specific volume (ft³/lbm or m³/kg)

Physical Significance

Enthalpy quantifies the energy required to create a system and make space for it by displacing its environment. In HVAC applications, enthalpy differences determine heat transfer requirements for heating, cooling, humidification, and phase change processes.

For water/steam systems, enthalpy serves as the primary property for:

• Boiler energy input calculations
• Condensate return energy recovery
• Steam trap sizing and selection
• Heat exchanger thermal analysis
• Turbine work output determination

Entropy (s)

Entropy measures the thermal energy per unit temperature unavailable for performing useful work, representing the degree of molecular disorder:

ds = δQ/T (for reversible processes)

Where:

• s = specific entropy (Btu/lbm·°R or kJ/kg·K)
• δQ = differential heat transfer (Btu or kJ)
• T = absolute temperature (°R or K)

Physical Significance

Entropy quantifies:

• Irreversibility of real processes
• Quality degradation of energy during conversion
• Direction of spontaneous processes (second law of thermodynamics)
• Maximum theoretical work obtainable from a heat engine
• Minimum theoretical work required for refrigeration

In HVAC systems, entropy analysis enables:

• Identification of major inefficiency sources
• Optimization of component performance
• Evaluation of thermodynamic perfection (isentropic efficiency)
• Second-law analysis of system performance

Water Phase Relationships

Saturation Conditions

At saturation, liquid and vapor phases coexist in thermodynamic equilibrium. Saturation temperature and pressure are dependent properties—specifying one fixes the other.

Subcooled (Compressed) Liquid

Liquid water below saturation temperature at a given pressure. Properties approximately equal saturated liquid properties at the same temperature:

h_f ≈ h_f@T (pressure effect negligible for most HVAC applications)

Typical applications:

• Condensate in steam systems (below saturation)
• Chilled water systems (35-50°F)
• Hot water heating systems (120-250°F)
• Boiler feedwater (prior to economizer)

Saturated Liquid

Liquid water at saturation temperature for a given pressure, ready to vaporize with any additional heat input. Properties denoted with subscript “f”:

• h_f = enthalpy of saturated liquid (Btu/lbm or kJ/kg)
• s_f = entropy of saturated liquid (Btu/lbm·°R or kJ/kg·K)

Saturated Vapor

Vapor at saturation temperature for a given pressure, ready to condense with any heat removal. Properties denoted with subscript “g”:

• h_g = enthalpy of saturated vapor (Btu/lbm or kJ/kg)
• s_g = entropy of saturated vapor (Btu/lbm·°R or kJ/kg·K)

Superheated Vapor

Vapor above saturation temperature at a given pressure. Temperature and pressure are independent properties in the superheat region. Degree of superheat:

Δt_superheat = t_actual - t_sat@P

Applications:

• Power generation turbine inlet steam (high superheat)
• Steam heating systems (minimal superheat, typically 5-15°F)
• Refrigeration compressor discharge (30-80°F superheat)

Latent Heat of Vaporization (h_fg)

The energy required to convert saturated liquid to saturated vapor at constant temperature and pressure:

h_fg = h_g - h_f

Temperature dependence of latent heat:

Note: Latent heat decreases with increasing temperature, reaching zero at the critical point (705.4°F, 3206.2 psia).

Quality (Dryness Fraction)

For two-phase mixtures, quality (x) defines the mass fraction of vapor:

x = m_vapor / (m_liquid + m_vapor)

Range: 0 ≤ x ≤ 1

• x = 0: saturated liquid
• 0 < x < 1: two-phase mixture
• x = 1: saturated vapor

Properties in the two-phase region:

h = h_f + x·h_fg

s = s_f + x·s_fg

v = v_f + x·v_fg

Steam quality considerations in HVAC:

• Boiler steam quality: x ≥ 0.98 minimum (ASME guidelines)
• Steam heating systems: x ≥ 0.95 recommended
• Steam turbines: x ≥ 0.88 at exhaust (erosion prevention)
• Flash steam recovery: quality calculation determines flash quantity

Temperature and Pressure Relationships

Clausius-Clapeyron Equation

Describes the relationship between saturation pressure and temperature:

dP/dT = h_fg / (T·v_fg)

Or in integrated approximation form:

ln(P₂/P₁) = (h_fg/R_v)·(1/T₁ - 1/T₂)

Where:

• P = saturation pressure (absolute)
• T = saturation temperature (absolute)
• h_fg = latent heat of vaporization
• v_fg = difference in specific volume (v_g - v_f)
• R_v = specific gas constant for water vapor (0.1102 Btu/lbm·°R or 461.5 J/kg·K)

Pressure-Temperature Correlation

For water/steam, saturation pressure increases exponentially with temperature:

Thermodynamic Region Identification

Given temperature and pressure, determine the phase:

1. Compare actual pressure to saturation pressure at given temperature
2. If P < P_sat@T: superheated vapor
3. If P = P_sat@T: saturation (may be liquid, vapor, or mixture)
4. If P > P_sat@T: compressed liquid

Alternatively, compare temperature to saturation temperature at given pressure:

1. If T > T_sat@P: superheated vapor
2. If T = T_sat@P: saturation
3. If T < T_sat@P: compressed liquid

Property Tables

Saturated Water Table (Temperature Basis)

Representative values for HVAC applications:

Reference: ASHRAE Handbook—Fundamentals, Chapter 30, Thermophysical Properties of Refrigerants

Saturated Water Table (Pressure Basis)

Common HVAC steam pressures:

Superheated Steam Table

Selected values for typical HVAC steam heating applications:

At 25 psig (39.696 psia):

At 100 psig (114.696 psia):

Compressed Liquid Water

For pressures significantly above saturation pressure at a given temperature, enthalpy and entropy corrections may be necessary:

h(T,P) ≈ h_f(T) + v_f(T)·(P - P_sat)

For most HVAC applications (P < 500 psia), the pressure correction is negligible:

• At 200°F and 100 psia: h ≈ 168.04 Btu/lbm (error < 0.5%)
• At 200°F and 500 psia: h ≈ 168.7 Btu/lbm (correction ~0.6 Btu/lbm)

Compressed liquid approximation is acceptable for:

• Boiler feedwater systems
• Hot water heating systems
• Chilled water systems
• Condensate return calculations

ASHRAE and Code References

ASHRAE Standards

ASHRAE Handbook—Fundamentals, Chapter 30: Thermophysical Properties of Refrigerants

• Comprehensive water/steam property tables
• Saturation and superheat data
• Thermodynamic diagrams
• Property correlations and equations

ASHRAE Standard 41.6: Standard Method for Measurement of Moist Air Properties

• Psychrometric calculations involving water vapor
• Enthalpy of moist air mixtures
• Humidity ratio determination

ASHRAE Guideline 2: Engineering Analysis of Experimental Data

• Uncertainty analysis for property measurements
• Data correlation methodology

ASME Standards

ASME Steam Tables (ASME International Steam Tables—IAPWS-IF97)

• Industrial standard for water/steam properties
• Temperature range: 0-800°C (32-1472°F)
• Pressure range: 0-100 MPa (0-14,500 psia)
• Accuracy: ±0.03% for most properties

ASME Power Test Code PTC 19.3: Temperature Measurement

• Instrumentation requirements for steam systems
• Measurement uncertainty quantification

ASME Boiler and Pressure Vessel Code (BPVC)

• Section I: Power Boilers (steam quality requirements)
• Section IV: Heating Boilers (low-pressure systems)

Industry References

Spirax Sarco Steam Engineering Tutorials

• Practical steam system design
• Steam quality and dryness considerations
• Condensate management

Department of Energy (DOE) Steam System Best Practices

• Energy efficiency optimization
• Steam trap management
• Condensate recovery economics

Design Considerations for Steam Systems

Steam Quality Requirements

Minimum steam quality (dryness fraction) varies by application:

Low steam quality consequences:

• Water hammer (safety hazard, equipment damage)
• Erosion of valves, traps, and piping
• Reduced heat transfer efficiency
• Thermal stress from temperature variation
• Process quality degradation

Enthalpy Drop Calculations

For steam heating applications, the enthalpy change determines heat transfer:

Q = ṁ·(h₁ - h₂)

Where:

• Q = heat transfer rate (Btu/hr or kW)
• ṁ = mass flow rate (lbm/hr or kg/s)
• h₁ = inlet steam enthalpy (Btu/lbm or kJ/kg)
• h₂ = outlet condensate enthalpy (Btu/lbm or kJ/kg)

Example: Steam Coil Calculation

Given:

• Steam supply: 25 psig saturated steam
• Condensate return: saturated liquid at 25 psig
• Heat load: 1,000,000 Btu/hr

Solution:

From tables at 25 psig (39.696 psia):

• t_sat = 267.2°F
• h_g = 1169.8 Btu/lbm
• h_f = 236.0 Btu/lbm

Enthalpy drop: h_fg = 1169.8 - 236.0 = 933.8 Btu/lbm

Steam flow required: ṁ = Q / h_fg = 1,000,000 / 933.8 = 1071 lbm/hr

If condensate subcools to 200°F: h₂ = 168.04 Btu/lbm Δh = 1169.8 - 168.04 = 1001.8 Btu/lbm ṁ = 1,000,000 / 1001.8 = 998 lbm/hr (6.8% reduction)

Flash Steam Recovery

When high-pressure condensate is reduced to lower pressure, a portion flashes to steam. The flash steam percentage is determined by enthalpy balance:

x_flash = (h_f1 - h_f2) / h_fg2

Where:

• x_flash = mass fraction flashing to steam
• h_f1 = liquid enthalpy at high pressure
• h_f2 = liquid enthalpy at low pressure
• h_fg2 = latent heat at low pressure

Example: Flash Steam Calculation

Given:

• Condensate at 100 psig (309.9 Btu/lbm)
• Flashes to 15 psig
• Condensate flow: 5000 lbm/hr

Solution:

At 100 psig: h_f1 = 309.9 Btu/lbm At 15 psig: h_f2 = 218.8 Btu/lbm, h_fg2 = 945.4 Btu/lbm

Flash fraction: x = (309.9 - 218.8) / 945.4 = 0.0964 or 9.64%

Flash steam flow: ṁ_flash = 5000 × 0.0964 = 482 lbm/hr

Recoverable energy (if flashed steam utilized): Q = 482 × 945.4 = 455,682 Btu/hr

Isentropic Efficiency

For expansion devices (turbines, expanders), isentropic efficiency compares actual performance to ideal reversible (constant entropy) expansion:

η_isentropic = (h₁ - h₂_actual) / (h₁ - h₂_isentropic)

For compression devices (pumps, compressors):

η_isentropic = (h₂_isentropic - h₁) / (h₂_actual - h₁)

Typical isentropic efficiencies:

• Large steam turbines: 85-92%
• Small steam turbines: 65-80%
• Centrifugal pumps: 70-85%
• Boiler feed pumps: 75-88%

Condensate Return System Design

Condensate enthalpy represents significant recoverable energy:

Energy Recovery = ṁ_condensate × (h_condensate - h_makeup)

At 212°F (atmospheric flash tank):

• Condensate enthalpy: 180.1 Btu/lbm
• Makeup water at 60°F: 28.06 Btu/lbm
• Recoverable energy: 152.0 Btu/lbm

For a system condensing 10,000 lbm/hr steam:

• Energy recovery: 10,000 × 152.0 = 1,520,000 Btu/hr
• Annual savings at $8/MMBtu: 1.52 × 8760 × 8 = $106,598/year

Return temperature considerations:

• Maximum recommended: 200-212°F (prevents cavitation)
• Minimum recommended: 130°F (maintains system cleanliness)
• Optimal for deaeration: 180-212°F

Entropy Analysis for System Optimization

Entropy generation identifies irreversibilities and optimization opportunities:

ΔS_gen = Σ(ṁ·s)_out - Σ(ṁ·s)_in + Q/T_boundary

For adiabatic systems (Q = 0):

ΔS_gen = Σ(ṁ·s)_out - Σ(ṁ·s)_in ≥ 0

Major sources of entropy generation in steam systems:

1. Throttling losses (pressure reducing valves): 15-30%
2. Heat transfer across finite temperature differences: 25-40%
3. Mixing of streams at different conditions: 5-15%
4. Friction in piping and equipment: 10-20%
5. Unrecovered condensate energy: 15-25%

Example: Throttling Loss Analysis

Given:

• Steam at 100 psig, saturated (338°F, 1190.9 Btu/lbm)
• Throttled to 15 psig (250.3°F saturation)
• Flow rate: 2000 lbm/hr

Solution:

At 100 psig (sat): h₁ = 1190.9 Btu/lbm, s₁ = 1.6962 Btu/lbm·°R

Throttling is isenthalpic: h₂ = h₁ = 1190.9 Btu/lbm

At 15 psig:

• h_f = 218.8 Btu/lbm, h_fg = 945.4 Btu/lbm, h_g = 1164.2 Btu/lbm
• s_f = 0.3679 Btu/lbm·°R, s_fg = 1.4453 Btu/lbm·°R

Since h₂ > h_g at 15 psig, steam is superheated after throttling.

Using superheat table at 15 psig, 290°F (approximate): s₂ ≈ 1.7850 Btu/lbm·°R

Entropy generation: ΔS_gen = s₂ - s₁ = 1.7850 - 1.6962 = 0.0888 Btu/lbm·°R

Total rate: 2000 × 0.0888 = 177.6 Btu/hr·°R

Exergy destruction at T₀ = 70°F (529.67°R): Ẋ_destroyed = T₀ × ΔṠ_gen = 529.67 × 177.6 = 94,069 Btu/hr

Alternative: Replace PRV with back-pressure turbine or mechanical work extraction device.

Practical Applications

Psychrometric Calculations

Water vapor enthalpy in air-water vapor mixtures:

h_a = h_da + W·h_g

Where:

• h_a = enthalpy of moist air (Btu/lbm dry air)
• h_da = enthalpy of dry air ≈ 0.240·t (Btu/lbm dry air)
• W = humidity ratio (lbm water vapor/lbm dry air)
• h_g = enthalpy of water vapor at dry-bulb temperature (Btu/lbm)

For standard psychrometric calculations, h_g is approximated:

h_g ≈ 1061 + 0.444·t (Btu/lbm) at temperatures from 32-100°F

This represents saturated vapor enthalpy plus superheat correction.

Boiler Efficiency Calculations

Direct method (input-output):

η_boiler = ṁ_steam·(h_steam - h_feedwater) / (ṁ_fuel × HHV_fuel)

Heat balance method includes all losses:

• Stack (flue gas) losses: 10-20% (largest single loss)
• Radiation and convection losses: 1-3%
• Blowdown losses: 1-5%
• Unburned fuel losses: 0.5-2%

Target boiler efficiency:

• Fire-tube boilers: 75-82%
• Water-tube boilers: 80-85%
• Condensing boilers: 90-96%

Deaerator Performance

Deaerators remove dissolved oxygen and CO₂ from feedwater by heating to saturation temperature, releasing non-condensable gases.

Operating pressure selection:

Enthalpy balance for steam consumption:

ṁ_steam·h_steam + ṁ_makeup·h_makeup + ṁ_condensate·h_condensate = (ṁ_steam + ṁ_makeup + ṁ_condensate)·h_deaerator

Typical dissolved oxygen targets:

• < 0.005 ppm for boilers > 900 psig
• < 0.04 ppm for boilers 300-900 psig
• < 0.3 ppm for boilers < 300 psig

Steam Turbine Work Output

For steam turbines, work output is the enthalpy drop:

W_turbine = ṁ·(h_inlet - h_exhaust)_actual

With isentropic efficiency:

h_exhaust,actual = h_inlet - η_s·(h_inlet - h_exhaust,isentropic)

Where h_exhaust,isentropic is found at exhaust pressure and s = s_inlet.

Back-pressure vs. condensing turbines:

• Back-pressure: exhaust steam used for process (higher pressure, lower work)
• Condensing: maximum work extraction (vacuum exhaust, 1-2 psia)

Conclusion

Enthalpy and entropy are fundamental properties for HVAC system analysis, design, and optimization. Accurate property evaluation using steam tables, understanding phase relationships, and applying thermodynamic principles enable:

• Precise energy balance calculations
• Efficient steam system design
• Optimization of component performance
• Identification of energy recovery opportunities
• Economic analysis of system improvements

Mastery of water/steam thermodynamic properties is essential for HVAC professionals involved in steam heating systems, boiler plants, power generation, and industrial process applications.