---
title: "Saturation curve on P-v and T-v diagrams"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 3
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:saturation-curve-pv-tv-sketch"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/saturation-curve-pv-tv-sketch
site: BCT Engineering
---

# Saturation curve on P-v and T-v diagrams

Fundamental of Thermodynamics & Heat Transfer · Chapter 3: Properties of Common Substances

- Asked in: 2070 Magh, 4 marks
- Video: [T-v Diagrams and PROPERTY TABLES for Thermodynamics in 13 Minutes!](https://www.youtube.com/watch?v=iZbnY0QWHe8) — Less Boring Lectures
- 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-pv-tv-sketch
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-3

## Question

Sketch the saturation curve on P-v and T-v diagram with all important points, lines and regions.

## Short answer

The saturation curve (vapor dome) on P-v and T-v diagrams is bounded by saturated liquid (x=0) and saturated vapor (x=1) lines meeting at the critical point. Inside is the two-phase wet mixture where isotherms (P-v) and isobars (T-v) are horizontal. Left: compressed liquid; right: superheated vapor.

## Answer

The saturation curve (vapour dome) is the boundary of the liquid-vapour two-phase region. It is formed by joining the saturated liquid states and the saturated vapour states for all pressures.

#### P-v diagram
```text
 P|            CP (critical point)
  |          .-*-.   T > Tc
  |         /     \_______
  | liquid /  wet   \____  T2 (isotherm)
  |  x=0  |  mixture  | x=1   superheated
  |  ||   |-----------|------ T1 (horizontal
  |  ||   |           |        in wet region)
  +------------------------------- v
```

#### T-v diagram
```text
 T|                  CP
  |                .--*--.                    / P2
  |               /       \               _.-'
  |          2f  /---------\ 2g ___.--'''       / P1
  |             /           \               _.-'
  |        1f  /-------------\ 1g ___.--'''
  |           /     wet       \
  |          /    mixture      \
  |  compressed               superheated
  |    liquid                   vapour
  +--------------------------------------------- v
      x = 0 line           x = 1 line
  (P2 > P1; in the liquid region the isobars lie almost on the x = 0 line)
```

**Important points, lines and regions**
- **Critical point (CP):** top of the dome (water: 22.09 MPa, 374.1 °C).
- **Saturated liquid line (x = 0):** left boundary; **saturated vapour line (x = 1):** right boundary.
- **Compressed (sub-cooled) liquid region:** left of the x = 0 line.
- **Wet (two-phase) region:** inside the dome; isotherms on P-v and isobars on T-v are horizontal here.
- **Superheated vapour region:** right of the x = 1 line.
- On P-v, an isotherm falls steeply in the liquid region, runs horizontally across the dome, then falls more gently in the superheated region. On T-v, an isobar rises steeply in the liquid region, runs horizontally across the dome, then rises again in the superheated region. The critical isotherm (P-v) and critical isobar (T-v) each have a point of inflection at CP.
- The triple line (solid, liquid and vapour together) lies at the bottom of the full diagram.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Left of x = 0:
   A. Superheated vapour
   B. Compressed liquid
   C. Wet mixture
   D. Solid
   Answer: B. Right of x = 1 is superheated. (Key point: Regions)

2. Isotherms on P-v in the dome are:
   A. Vertical
   B. Rising
   C. Horizontal
   D. Hyperbolic
   Answer: C. Boil at Psat. (Key point: Inside dome)

3. Critical isotherm at CP:
   A. Is horizontal throughout
   B. Has none
   C. Is vertical
   D. Has inflection with horizontal tangent
   Answer: D. Above Tc no phase change. (Key point: Critical isotherm)

4. CP is:
   A. Top of dome where x=0 and x=1 meet
   B. Bottom of dome
   C. Triple point
   D. x=0.5
   Answer: A. Water 22.09 MPa. (Key point: Critical point)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Saturation curve on T-v diagram](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-curve-tv-diagram) — Fundamental of Thermodynamics & Heat Transfer, chapter 3, asked 2×
- [Saturation curve with isobars on T-v](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-curve-isobars-tv) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
- [Define saturation pressure, saturated liquid, etc.; sketch](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-pressure-saturated-liquid-defs) — Fundamental of Thermodynamics & Heat Transfer, chapter 3

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