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

# Saturation curve with isobars on T-v

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

- Asked in: 2069 Bhadra, 6 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-isobars-tv
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-3

## Question

Sketch saturation curve of water in T-v with the help of isobar lines. Show all important points, lines and region. Also define saturation temperature and quality.

## Short answer

The T-v saturation curve is a dome with x=0 and x=1 lines meeting at the critical point; inside, isobars are horizontal. Saturation temperature is the boiling point at a given pressure. Quality is the vapor mass fraction in a mixture, x=m_g/m.

## Answer

#### Saturation curve with isobars on T-v diagram
When water is heated at constant pressure, the process follows an isobar. At low pressure the isobar has a long horizontal portion; at higher pressure the horizontal portion is shorter and at a higher temperature, and at the critical pressure it shrinks to a point of inflection at the critical point.

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

**Regions and lines**
- **Left of x = 0 (saturated liquid line):** compressed liquid.
- **Dome interior:** two-phase mixture; isobars are horizontal at T_sat.
- **Right of x = 1:** superheated vapour.
- **Critical point:** the top of the dome, where the x = 0 and x = 1 lines meet.
- Along an isobar: the liquid warms up (T rises, v nearly constant), evaporates at constant T_sat (v from v_f to v_g), and then the vapour is superheated (T and v both rise).

#### Saturation temperature
The temperature at which a pure substance boils (or condenses) at a given pressure. T_sat rises with pressure; for water it is 100 °C at 101.3 kPa and 179.9 °C at 1 MPa.

#### Quality
The ratio of the mass of vapour to the total mass of the mixture, x = m_g/(m_f + m_g). It varies from 0 (saturated liquid) to 1 (saturated vapour) and is used in v = v_f + x v_fg.

## Check yourself

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

1. Along an isobar:
   A. T constant throughout
   B. T rises, flat at Tsat, then T rises
   C. T falls
   D. v constant
   Answer: B. Evaporates at constant T. (Key point: Isobar stages)

2. Higher pressure isobar:
   A. Longer flat portion
   B. Same
   C. Higher Tsat, shorter flat portion
   D. Lower
   Answer: C. At Pc it becomes inflection. (Key point: High pressure)

3. Tsat of water at 1 MPa:
   A. 100 C
   B. 374 C
   C. 120 C
   D. 179.9 C
   Answer: D. Rises with pressure. (Key point: Saturation temperature)

4. x varies:
   A. 0 to 1
   B. 0 to 100
   C. -1 to 1
   D. 1 to infinity
   Answer: A. v = vf + x vfg. (Key point: Quality)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [Saturation curve on P-v and T-v diagrams](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-curve-pv-tv-sketch) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
- [Define saturation temp, sub cooled liquid, quality, critical point](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asaturation-subcooled-quality-critical-defs) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
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- [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×
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