Properties

Thermodynamic properties define the state of a substance and govern energy transfer processes in HVAC systems. Understanding property classification, measurement, and calculation enables accurate system design and performance analysis.

Property Classification

Intensive Properties

Intensive properties are independent of system mass or extent. These properties remain constant when a system is divided:

Common Intensive Properties:

• Temperature (T)
• Pressure (P)
• Specific volume (v = V/m)
• Specific enthalpy (h = H/m)
• Specific entropy (s = S/m)
• Specific internal energy (u = U/m)
• Density (ρ = 1/v)
• Quality (x)

Extensive Properties

Extensive properties scale proportionally with system mass or extent:

Common Extensive Properties:

• Mass (m)
• Volume (V)
• Total enthalpy (H)
• Total entropy (S)
• Total internal energy (U)

Conversion Relationship:

Specific Property = Extensive Property / Mass
v = V/m
h = H/m
s = S/m

State Postulate

The state of a simple compressible substance is completely specified by two independent intensive properties. This fundamental principle enables property determination:

Requirements:

1. System must be in equilibrium
2. Properties must be independent
3. System must be simple compressible (no magnetic, electric, or surface tension effects)

Common Property Pairs:

• Temperature and pressure (T, P)
• Pressure and specific enthalpy (P, h)
• Temperature and specific entropy (T, s)
• Pressure and quality (P, x) for two-phase states

Primary Thermodynamic Properties

Internal Energy (u)

Molecular-scale energy of a substance, including kinetic and potential energy of molecules.

Units: kJ/kg, Btu/lbm

Enthalpy (h)

Combined property representing total energy content:

h = u + Pv

Where:

• h = specific enthalpy (kJ/kg)
• u = specific internal energy (kJ/kg)
• P = absolute pressure (kPa)
• v = specific volume (m³/kg)

Physical Meaning: Enthalpy represents the energy required to create the substance and make room for it by displacing the environment.

Entropy (s)

Measure of molecular disorder or energy dispersal.

Units: kJ/(kg·K), Btu/(lbm·°R)

Second Law Relationship:

ds ≥ δq/T

For reversible processes: ds = δq/T

Specific Heats

Constant Pressure (cp):

cp = (∂h/∂T)P

Constant Volume (cv):

cv = (∂u/∂T)v

Heat Capacity Ratio (k):

k = cp/cv

Equations of State

Equations relating pressure, temperature, and specific volume.

Ideal Gas Law

Pv = RT

Where:

• P = absolute pressure (kPa)
• v = specific volume (m³/kg)
• R = specific gas constant (kJ/kg·K)
• T = absolute temperature (K)

Gas Constant:

R = R̄/M

R̄ = universal gas constant = 8.314 kJ/(kmol·K) M = molar mass (kg/kmol)

Valid When:

• Low pressure (P < 1 MPa for most gases)
• High temperature (T > 2Tcritical)
• Gases far from saturation

Van der Waals Equation

Corrects ideal gas law for molecular size and intermolecular forces:

(P + a/v²)(v - b) = RT

Where:

• a = attraction parameter
• b = molecular volume parameter

Compressibility Factor (Z)

Measures deviation from ideal gas behavior:

Z = Pv/RT

• Z = 1: ideal gas behavior
• Z < 1: attractive forces dominate (common at moderate pressures)
• Z > 1: repulsive forces dominate (common at high pressures)

Property Tables and Data Sources

Saturated Property Tables

Organize properties along the saturation curve where liquid and vapor coexist.

Table Entry Format:

Subscripts:

• f = saturated liquid
• g = saturated vapor
• fg = difference (evaporation)

Superheated Vapor Tables

Properties of vapor above saturation temperature at given pressure.

Example: Superheated R-134a

Compressed Liquid Tables

Properties of liquid below saturation temperature at given pressure. Often approximated using saturated liquid properties at the same temperature.

Refrigerant Properties

Critical Properties

Properties at the critical point where liquid-vapor distinction vanishes.

Normal Boiling Points

Property Calculation in Two-Phase Region

When quality (x) is known:

v = vf + x·vfg = vf + x(vg - vf)
h = hf + x·hfg
s = sf + x·sfg
u = uf + x·ufg

Where x = mass fraction of vapor (0 ≤ x ≤ 1)

Quality Determination:

x = (v - vf)/(vg - vf)
x = (h - hf)/(hg - hf)
x = (s - sf)/(sg - sf)

Property Relationships

Maxwell Relations

Derived from exactness of thermodynamic properties:

(∂T/∂v)s = -(∂P/∂s)v
(∂T/∂P)s = (∂v/∂s)P
(∂P/∂T)v = (∂s/∂v)T
(∂v/∂T)P = -(∂s/∂P)T

Clapeyron Equation

Relates saturation pressure and temperature:

dPsat/dT = hfg/(T·vfg)

This equation governs the slope of phase boundaries on property diagrams.

Property Diagrams

Temperature-Entropy (T-s) Diagram

• X-axis: specific entropy (s)
• Y-axis: temperature (T)
• Shows constant pressure lines
• Area under process curve = heat transfer for reversible process
• Useful for analyzing Carnot cycles and heat engines

Pressure-Enthalpy (P-h) Diagram

• X-axis: specific enthalpy (h)
• Y-axis: pressure (P, logarithmic scale)
• Standard diagram for refrigeration cycle analysis
• Horizontal lines = constant pressure processes
• Vertical lines = constant enthalpy (throttling) processes
• Quality lines radiate from critical point

Pressure-Volume (P-v) Diagram

• X-axis: specific volume (v)
• Y-axis: pressure (P)
• Area under process curve = boundary work
• Shows isothermal and isentropic processes clearly

Mollier Diagram (h-s)

• X-axis: specific entropy (s)
• Y-axis: specific enthalpy (h)
• Useful for steam turbine and compressor analysis
• Constant pressure lines slope upward
• Constant temperature lines horizontal in two-phase region

Components

• Enthalpy Calculations
• Entropy Calculations
• Internal Energy
• Specific Heat Constant Pressure
• Specific Heat Constant Volume
• Heat Capacity Ratio
• Compressibility Factor
• Reduced Properties
• Corresponding States
• Virial Equations
• Equations Of State
• Ideal Gas Law
• Van Der Waals Equation
• Redlich Kwong Equation
• Peng Robinson Equation
• Benedict Webb Rubin Equation
• Property Tables Charts
• Mollier Diagrams
• Ts Diagrams
• Ph Diagrams
• Pv Diagrams