--- title: "Saturation curve on T-v diagram" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 3 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:saturation-curve-tv-diagram" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/saturation-curve-tv-diagram site: BCT Engineering --- # Saturation curve on T-v diagram Fundamental of Thermodynamics & Heat Transfer · Chapter 3: Properties of Common Substances - Asked in: 2072 Asoj, 4 marks; 2071 Bhadra, 4 marks (asked 2 times) - Video: [Pure Substances - T V Diagram](https://www.youtube.com/watch?v=0srmqfcO4HI) — TutorialsPoint - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/saturation-curve-tv-diagram - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-3 ## Question Explain saturation curve of two-phase mixture on T-v diagram. ## Short answer The saturation curve on a T-v diagram is a dome formed by saturated liquid (x=0) and saturated vapor (x=1) lines meeting at the critical point. Below is the wet mixture region where temperature stays constant during phase change. Left is compressed liquid, right is superheated vapor. ## Answer A pure substance such as water, heated at constant pressure, changes from liquid to vapour at the saturation temperature of that pressure. If the states at which boiling starts and ends are joined for several pressures, we get the **saturation (vapour dome) curve** on the T-v diagram. ```text T| CP (critical point) | .--*--. | / \ | liquid wet \ superheated | | x=0 mixture x=1 vapour | | 1-------2 | | | (isobar) | +------------------------ v ``` **Features** - **Saturated liquid line (x = 0):** left part of the dome, states at which the liquid is about to boil (v = v_f). - **Saturated vapour line (x = 1):** right part, states at which the last liquid has vaporised (v = v_g). - **Critical point:** the top where the two lines meet; at P_c = 22.09 MPa, T_c = 374 °C for water, there is no distinct liquid-vapour change. - **Left of x = 0:** compressed (sub-cooled) liquid region. - **Under the dome:** wet (two-phase) mixture of liquid and vapour; T = T_sat(P) and v = v_f + x v_fg. The isobar is horizontal here. - **Right of x = 1:** superheated vapour region. - On a constant pressure line, T rises in the liquid, stays constant during evaporation (v_f to v_g), then rises again as vapour is superheated. Higher-pressure isobars have higher saturation temperatures and a shorter horizontal segment, which vanishes at the critical point. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What do the left and right sides of the dome on the T-v diagram represent? A. Left is saturated liquid (x = 0, v = vf); right is saturated vapour (x = 1, v = vg) B. Left is saturated vapour; right is saturated liquid C. Left is compressed liquid; right is superheated vapour D. Both are wet mixture boundaries at x = 0.5 Answer: A. Joining boiling-start states gives the x = 0 line on the left and the end-of-boiling states give the x = 1 line on the right. (Key point: Dome lines) 2. What does a constant-pressure line look like inside the dome? A. Vertical at constant v B. Horizontal at T = Tsat(P) while v goes from vf to vg C. Rising steeply as the mixture heats D. A curve identical to an isotherm in the superheated region Answer: B. During evaporation at constant pressure the temperature stays at Tsat while the volume increases. (Key point: Isobar inside dome) 3. What happens at the critical point at the top of the dome? A. The wet region is widest B. Quality is always 0.5 C. Saturated liquid and vapour lines meet; no distinct liquid-vapour change D. The substance freezes Answer: C. At the critical point (22.09 MPa, 374 C for water) the two phases become identical. (Key point: Critical point) 4. How does a higher-pressure isobar differ? A. Lower Tsat and a longer horizontal segment B. Same Tsat but shifted right C. No change since boiling is independent of pressure D. Higher Tsat and a shorter horizontal segment, vanishing at the critical point Answer: D. Raising pressure raises saturation temperature and shortens the evaporation segment until it disappears at the critical pressure. 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