Steam Tables — Interactive Reference

Linear Interpolation Across All Table Columns

f = (X − X_1) / (X_2 − X_1) | 0 < f < 1 | Y = Y_1 + f · (Y_2 − Y_1) | applied with the same f to every column of the two bracketing rows

Variables: X = target value of the table's leading (independent) column — temperature (°C) on the saturated-by-temperature and superheated tabs, pressure (kPa) on the saturated-by-pressure tab; X_1, X_2 = leading-column values of the two rows that bracket X (X_1 < X < X_2) within the rows currently displayed, i.e. after any filter is applied — the filter narrows both the valid range and the available brackets; f = interpolation fraction (dimensionless, strictly between 0 and 1 — an exact table match, or a target outside the displayed range, produces no interpolated row); Y = interpolated value of any column: P_sat (kPa) or T_sat (°C), v_f, v_g, v (m³/kg), h_f, h_fg, h_g, h, u_f, u_fg, u_g, u (kJ/kg), s_f, s_fg, s_g, s (kJ/(kg·K)); Y_1, Y_2 = that column's values in the bracketing rows (same units as Y); interpolated values are shown to 6 significant figures. The rows themselves are exact IAPWS-IF97 values printed to 5 significant figures (pressure, specific volume), 0.01 kJ/kg (h, u) and 0.0001 kJ/(kg·K) (s); only values between rows are interpolated. Sources: IAPWS R7-97(2012) (row values); Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 'Properties of Pure Substances' (linear interpolation between property-table entries)

Saturation Temperature from Pressure (by-pressure tab)

T_sat(P) = T_1 + [(P − P_1) / (P_2 − P_1)] · (T_2 − T_1)

Variables: P = target saturation pressure (kPa); the full tabulation spans 0.611657 kPa (triple point) to 22064 kPa (critical point), but interpolation is carried out only over the rows left visible by the pressure filter (which keeps rows within ±50% of the filter value), so an unfiltered table is required to reach the full span; P_1, P_2 = bracketing tabulated saturation pressures (kPa); T_1, T_2 = tabulated saturation temperatures at P_1 and P_2 (°C); T_sat = interpolated saturation temperature (°C). Accuracy note: P_sat(T) is close to exponential, so linear interpolation in P is a first-order fit; over the coarse 5000-7500-10000-15000-20000 kPa spacing it reads about 1 °C low (6000 kPa gives 274.58 °C against 275.59 °C from IAPWS-IF97). Interpolating ln(P) against 1/T is the accurate practice. Source: Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 8th ed., Ch. 3 (saturation temperature-pressure correspondence; interpolation in the pressure-entry saturation table)

Saturation-Line Column Identities

h_g = h_f + h_fg | s_g = s_f + s_fg | u_g = u_f + u_fg

Variables: h_g, h_f, h_fg = saturated-vapour enthalpy, saturated-liquid enthalpy and enthalpy of vaporisation (kJ/kg); s_g, s_f, s_fg = the corresponding entropies (kJ/(kg·K)); u_g, u_f, u_fg = the corresponding internal energies (kJ/kg); subscript f = saturated liquid, subscript g = saturated vapour, subscript fg = the g − f difference. Each row comes from one IAPWS-IF97 evaluation with the fg column formed before rounding, so after each column is rounded the identities hold to within 0.01 kJ/kg for h and u and 0.0001 kJ/(kg·K) for s on every row. The interpolation applies one fraction f column-wise, so it carries that rounding residual through unchanged. Sources: IAPWS R7-97(2012); Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 (definition of the f, g and fg property columns)

Degree of Superheat on a Selected Isobar

ΔT_superheat = T − T_sat(P)

Variables: ΔT_superheat = degrees of superheat above the saturation temperature (K; numerically identical to a °C interval); T = steam temperature read from the superheated table (°C); T_sat(P) = IAPWS-IF97 saturation temperature of the selected isobar (°C), displayed in the pressure selector and info line — 99.61 at 100 kPa, 120.21 at 200, 143.61 at 400, 158.83 at 600, 179.89 at 1000, 212.38 at 2000, 263.94 at 5000, 311.00 at 10000 kPa; P = selected isobar pressure (kPa). The page shows T and T_sat side by side; the subtraction is left to the reader and is not evaluated by the tool. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 (superheated vapour; degrees of superheat relative to T_sat at the same pressure)