Properties and tables

Why it matters

Water and steam do a huge share of the world's engineering work: power plants, district heating, sterilisers, process heating and cooling towers. Unlike an ideal gas, water's properties near boiling cannot be written as one tidy equation you would use by hand, so engineers look them up in property tables (steam tables) or software built on the international IAPWS formulation. Reading these tables, and interpolating between rows, is a core skill tested in every thermodynamics course and on the FE exam.

State principle and phases

For a simple pure substance, two independent intensive properties fix the state. Temperature and pressure work for compressed liquidLiquid at a pressure above the saturation pressure for its temperature; often approximated by saturated liquid at the same temperature. or superheated vapourVapour at a temperature above saturation for its pressure, so its pressure is below the saturation pressure for its temperature., but not inside the dome: while water boils at a given pressure, its temperature stays at the saturation temperatureThe temperature at which a pure substance boils at a given pressure; it stays fixed while the liquid boils.. Inside the dome you need a second property such as the qualityThe mass fraction of a saturated mixture that is vapour, from x = 0 (saturated liquid) to x = 1 (saturated vapour). x, the mass fraction that is vapour (x = 0 saturated liquid, x = 1 saturated vapour).

The main table families are:

• Saturated water, by temperature and by pressure: properties of saturated liquid (subscript f) and saturated vapour (subscript g), plus the difference fg (for example hfg, the enthalpy of vaporisationhfg, the energy per kilogram needed to turn saturated liquid into saturated vapour at the same temperature.).
• Superheated vapour: blocks of rows at fixed pressure, for temperatures above saturation.
• Compressed liquid: often approximated by saturated liquid at the same temperature.

Reading a saturated table

Here are a few rows of a saturated-water table (values rounded, from standard textbook tables based on IAPWS):

T (°C)   Psat (kPa)   hf (kJ/kg)   hfg (kJ/kg)   hg (kJ/kg)
100      101.42       419.17       2256.4        2675.6
105      120.90       440.28       2243.1        2683.4
110      143.38       461.42       2229.7        2691.1
115      169.18       482.59       2216.0        2698.6
120      198.67       503.81       2202.1        2706.0

Check the consistency: hf + hfg = hg (419.17 + 2256.4 = 2675.6). For a wet mixture at quality x:

h = hf + x · hfg

So water at 100 °C with x = 0.5 has h = 419.17 + 0.5 × 2256.4 = 1547.4 kJ/kg.

Linear interpolation

Tables list values at steps. For a value between two rows, assume a straight line:

y = y1 + (x − x1) · (y2 − y1) / (x2 − x1)

Worked example: hf at 112 °C.

y = 461.42 + (112 − 110) · (482.59 − 461.42) / (115 − 110)
  = 461.42 + 2 · 21.17 / 5
  = 461.42 + 8.468 = 469.89 kJ/kg

The same formula works in either direction: you can find the temperature for a given enthalpy by swapping which column is x and which is y. Linear interpolationEstimating a value between two table rows by assuming a straight line between them. is accurate enough for most table steps, but it gets worse near the critical point, where properties change sharply.

Deciding which table to use

Given temperature T and pressure P:

1. Look up Psat at T (or Tsat at P).
2. If P > Psat, the water is a compressed liquid.
3. If P < Psat, it is a superheated vapour.
4. If P = Psat, it is a saturated mixture, and you need one more property (x, v, h or s) to fix the state.

For example, water at 120 °C and 500 kPa: Psat at 120 °C is 198.67 kPa, and 500 > 198.67, so it is a compressed liquid, and h ≈ hf at 120 °C ≈ 503.8 kJ/kg.

Other sources of properties

• NIST Chemistry WebBook offers free fluid property calculators for water and many refrigerants: https://webbook.nist.gov/chemistry/fluid/ (Checked on 2026-10-23.)
• CoolProp is an open-source property library you can call from Python on your own computer.
• Textbook tables differ slightly in the last digit and in the reference state (the zero point of h and s). Always take every property in a calculation from the same source.

Common mistakes

• Using the superheated table inside the dome. Check Psat first.
• Interpolating between rows of different pressure blocks in the superheated table without doing a double interpolation.
• Mixing reference states from two different tables or programs.
• Forgetting units. Tables give v in m³/kg, h and u in kJ/kg, s in kJ/(kg·K), P in kPa or MPa.

Recap

• Two independent properties fix a state; inside the dome T and P are not independent.
• h = hf + x·hfg for a wet mixture.
• Linear interpolation: y = y1 + (x − x1)(y2 − y1)/(x2 − x1).
• Compare P with Psat to choose the right table.

Try it

On the Do tab, write the interpolation formula and use it to look up saturated-water properties between table rows.