R-134a Properties Calculator

Two-Phase Lever Rule (state from quality)

v = v_f + x · (v_g − v_f); h = h_f + x · h_fg; s = s_f + x · s_fg; u = u_f + x · u_fg

Variables: x = quality, mass fraction of saturated vapour (dimensionless, 0 to 1); v = mixture specific volume (m³/kg); v_f, v_g = saturated-liquid and saturated-vapour specific volume (m³/kg); h = specific enthalpy (kJ/kg); h_f = saturated-liquid enthalpy (kJ/kg); h_fg = latent heat of vaporisation (kJ/kg); s = specific entropy (kJ/(kg·K)); s_f = saturated-liquid entropy (kJ/(kg·K)); s_fg = entropy of vaporisation (kJ/(kg·K)); u = specific internal energy (kJ/kg); u_f = saturated-liquid internal energy (kJ/kg); u_fg = internal energy of vaporisation (kJ/kg). Reference state is the one built into this table: h_f = −7.4 kJ/kg and s_f = −0.0339 kJ/(kg·K) at −40 °C, which matches neither the ASHRAE/IIR convention (h_f = 200 kJ/kg at 0 °C) nor the common textbook convention (h_f = 0 at −40 °C) — differences in h, s and u are valid, absolute values are not comparable with other tables. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 (saturated liquid–vapour mixture, quality); R-134a table data per ASHRAE Handbook — Fundamentals, thermophysical properties of refrigerants

Quality Back-Calculated from a Measured Property

x = (v − v_f) / (v_g − v_f); x = (h − h_f) / h_fg; x = (s − s_f) / s_fg; x = (u − u_f) / u_fg

Variables: x = quality (dimensionless, 0 to 1); v = measured specific volume (m³/kg); v_f, v_g = saturated-liquid and saturated-vapour specific volume (m³/kg); h = measured specific enthalpy (kJ/kg); h_f = saturated-liquid enthalpy (kJ/kg); h_fg = latent heat of vaporisation (kJ/kg); s = measured specific entropy (kJ/(kg·K)); s_f, s_fg = saturated-liquid and vaporisation entropy (kJ/(kg·K)); u = measured specific internal energy (kJ/kg); u_f, u_fg = saturated-liquid and vaporisation internal energy (kJ/kg). The calculator uses the tabulated h_fg, s_fg and u_fg columns as the denominator, and (v_g − v_f) for specific volume because the table carries no v_fg column. The state is classified as compressed liquid when the measured property is at or below its f value, two-phase when it lies between the f and g values, and superheated above the g value. Given a quality plus one of v, h, s or u, the same relation is inverted on temperature: the tool scans the saturation table for the T whose lever-rule mixture property equals the input, then interpolates linearly between the bracketing rows. Source: Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 8th ed., Ch. 3 (determining quality from v, u, h or s)

Saturation-Table Interpolation and Inverse Saturation Temperature

Y(T) = Y_i + (T − T_i) · (Y_(i+1) − Y_i) / (T_(i+1) − T_i); T_sat(P) = T_i + (P − P_i) · (T_(i+1) − T_i) / (P_(i+1) − P_i)

Variables: T = queried saturation temperature (°C); T_i, T_(i+1) = bracketing tabulated temperatures (°C); P = queried pressure (kPa); P_i, P_(i+1) = tabulated saturation pressures at T_i and T_(i+1) (kPa); Y = any saturation-table column — P_sat (kPa), v_f, v_g (m³/kg), h_f, h_fg, h_g, u_f, u_fg, u_g (kJ/kg), s_f, s_fg, s_g (kJ/(kg·K)); Y_i, Y_(i+1) = tabulated values at T_i and T_(i+1) (same units as Y); T_sat = saturation temperature at P (°C). Range and clamping: the saturation table spans −40 °C to the 101.06 °C critical point (51.8 to 4059.3 kPa). Inputs outside that band are clamped to the end row rather than extrapolated, so any P above 4059.3 kPa returns T_sat = 101.06 °C and any P below 51.8 kPa returns T_sat = −40 °C — supercritical states are not modelled. When T and P are supplied together and agree to within 0.5 °C of the saturation line the solver cannot resolve quality and returns the saturated liquid (x = 0). Compressed-liquid states return the saturated-liquid values at the same temperature, v ≈ v_f(T), h ≈ h_f(T), s ≈ s_f(T), u ≈ u_f(T); the h_f(T) + v_f(T)·(P − P_sat(T)) pressure correction is not applied. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 (interpolation in property tables; saturation temperature from saturation pressure; compressed-liquid approximation)

Superheated-Vapour Double (Bilinear) Table Interpolation

Y(P_j, T) = Y_(j,k) + (T − T_k) · (Y_(j,k+1) − Y_(j,k)) / (T_(k+1) − T_k); Y(P, T) = Y(P_lo, T) + (P − P_lo) · (Y(P_hi, T) − Y(P_lo, T)) / (P_hi − P_lo)

Variables: Y = superheated-table property being interpolated — v (m³/kg), h (kJ/kg), s (kJ/(kg·K)) or u (kJ/kg); T = queried temperature (°C); T_k, T_(k+1) = bracketing tabulated temperatures on isobar j (°C); Y_(j,k), Y_(j,k+1) = tabulated property values at those temperatures on isobar j (same units as Y); P = queried pressure (kPa); P_lo, P_hi = bracketing tabulated isobars (kPa), drawn from the set 60, 100, 200, 400, 600, 800, 1000, 1200 and 1600 kPa; Y(P_lo, T), Y(P_hi, T) = the temperature-interpolated values on those two isobars (same units as Y). The tool interpolates first in temperature within each isobar table, then linearly in pressure between the two isobars. Pressures outside 60–1600 kPa, and temperatures outside a given isobar's tabulated range, are clamped to the nearest tabulated isobar or row rather than extrapolated — a state well above 1600 kPa is returned at the 1600 kPa values and is not physically meaningful. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 3 (superheated vapour tables; double interpolation between tabulated pressures and temperatures)