Vapor and Vapor Tables

Vapor and vapor tables concern the thermodynamic properties of a pure substance in the two-phase region (liquid + vapor), the saturated states, and the single-phase vapor (superheated) region. Saturated liquid (often called ``wet'' or saturated liquid) and saturated vapor are the two bounding states on the saturation curve for a given pressure or temperature. A two-phase mixture is characterized by the dryness fraction (quality) x (mass fraction of vapor). Vapor tables (steam tables for water) tabulate properties at saturation (hf, hg, vf, vg, sf, sg, etc.) as functions of temperature or pressure and also provide superheated-vapor tables that give properties (h, s, v) at specified pressures and temperatures above the saturation temperature. Important practical uses include energy balances for boilers/turbines, isenthalpic throttling, and thermodynamic cycle analyses.

Governing FormulaKey relations and definitions (SI units unless noted): - Quality (dryness) x (mass fraction of vapor): x = (m_vapor) / (m_total) - Specific property of a saturated mixture (specific volume, enthalpy, entropy): v = v_f + x v_fg = v_f + x (v_g - v_f) h = h_f + x h_fg = h_f + x (h_g - h_f) s = s_f + x s_fg = s_f + x (s_g - s_f) (vf, vf are saturated liquid values; vg, hg, sg are saturated vapor values) - Clausius–Clapeyron (differential form) for the saturation curve: dp_sat/dT = h_fg / (T · Δv) where Δv = v_g - v_f (for vaporization Δv ≈ v_g so dp/dT ≈ h_fg/(T v_g) when vf ≪ vg) - Clausius–Clapeyron (approx. integrated form, assuming nearly constant latent heat): ln(p2/p1) ≈ - (L/R) (1/T2 - 1/T1) (L is specific latent heat per mass, R is gas constant of vapor) - Ideal-gas relation for vapor (when applicable): p v = R T (p in kPa, v in m^3/kg, R in kJ·kg⁻¹·K⁻¹ gives T in K since 1 kPa·m^3 = 1 kJ) - Isenthalpic throttling (steady-flow throttling valve): h_in = h_out (no heat/work, negligible kinetic/potential changes) Assumptions commonly used in problems: pure substance (water unless stated), properties given in tables when needed, small liquid specific volume relative to vapor where justified, and SI units (kPa, MPa, kJ·kg⁻¹, m^3·kg⁻¹, K).

Knowledge Check

10 Questions

1.Which statement correctly distinguishes a saturated vapor from a superheated vapor for a pure substance?

2.A saturated water mixture at 100°C has h_f = 419.0 kJ/kg and h_fg = 2257.0 kJ/kg. If the mixture specific enthalpy is 2200.0 kJ/kg, what is the dryness fraction x?

3.A saturated mixture of water at a certain pressure has vf = 0.00103 m^3/kg and v_g - v_f = v_fg = 0.500 m^3/kg. If the measured specific volume of the mixture is v = 0.300 m^3/kg, what is the quality x?

4.Assuming ideal-gas behavior for steam with R = 0.4615 kJ·kg⁻¹·K⁻¹, what is the temperature (in K) of steam at p = 200 kPa and specific volume v = 2.00 m^3/kg?

5.Which differential relation gives the slope of the saturation pressure curve dp_sat/dT for vaporization of a pure substance?

6.Using the approximate integrated Clausius–Clapeyron relation (constant L), estimate the saturation pressure at T2 = 398.15 K (125°C) given p1 = 101.325 kPa at T1 = 373.15 K (100°C), latent heat L = 2257 kJ/kg, and R = 0.4615 kJ·kg⁻¹·K⁻¹. (Use ln(p2/p1) = (L/R)(1/T1 - 1/T2).)

7.A superheated-steam table excerpt at 300 kPa gives specific enthalpy h = 2850 kJ/kg at 300°C and h = 3000 kJ/kg at 350°C. Using linear interpolation, what is h at 320°C (assume linear variation between these two points)?

8.Steam initially at 5 MPa is dry saturated vapor with s1 = 6.50 kJ·kg⁻¹·K⁻¹ and expands isentropically to 0.1 MPa. At 0.1 MPa the saturated properties are s_f = 1.307 kJ·kg⁻¹·K⁻¹ and s_g = 7.359 kJ·kg⁻¹·K⁻¹. What is the quality x at the turbine exit?

9.Saturated water at 1.0 MPa with quality x1 = 0.20 is throttled (isenthalpic) to 0.10 MPa. Given at 1.0 MPa: h_f = 762.0 kJ/kg and h_g = 2778.0 kJ/kg; at 0.10 MPa: h_f' = 417.5 kJ/kg and h_g' = 2676.0 kJ/kg. What is the outlet quality x2 at 0.10 MPa?

10.Which description correctly locates regions on a T-v diagram for a pure substance?