---
title: "Quality, moisture content, specific volume of mixture"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 3
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:quality-moisture-specific-volume"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/quality-moisture-specific-volume
site: BCT Engineering
---

# Quality, moisture content, specific volume of mixture

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

- Asked in: 2074 Bhadra, 4 marks
- Video: [Steam Tables: Calculating Quality](https://www.youtube.com/watch?v=J6LgIO3qdO0) — LearnChemE
- 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/quality-moisture-specific-volume
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-3

## Question

Define quality and moisture content. Derive an expression for specific volume of a two phase mixture in terms of quality.

## Short answer

Quality x is mass fraction of vapor in a two-phase mixture. Specific volume is v = v_f + x v_fg = (1−x)v_f + x v_g, where v_f, v_g are saturated liquid and vapor specific volumes.

## Answer

#### Quality (dryness fraction), x
For a saturated liquid-vapour mixture, quality is the ratio of the mass of vapour to the total mass of the mixture:

x = m_g / (m_f + m_g) = m_g / m

It is 0 for saturated liquid and 1 for saturated vapour. It is defined only in the two-phase region.

#### Moisture content
The mass fraction of liquid in the mixture: = m_f / m = **1 − x**.

#### Specific volume of a two-phase mixture
Let the mixture have total mass m = m_f + m_g, and total volume V = V_f + V_g.

V = m_f v_f + m_g v_g

Divide by m, using m_f/m = (1 − x) and m_g/m = x:

v = (1 − x) v_f + x v_g

**v = v_f + x (v_g − v_f) = v_f + x v_fg**

Here v_f and v_g are the specific volumes of saturated liquid and vapour at the given pressure or temperature, and v_fg = v_g − v_f. Hence x = (v − v_f)/v_fg. The same form applies to u, h and s.

## Check yourself

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

1. What is quality x?
   A. Mass of vapour divided by total mass of the mixture
   B. Volume of vapour divided by total volume
   C. Mass of liquid divided by total mass
   D. Mass of vapour divided by mass of liquid
   Answer: A. x = mg/(mf + mg); it is 0 for saturated liquid and 1 for saturated vapour. (Key point: Quality definition)

2. Moisture content equals:
   A. x
   B. 1 - x
   C. x/(1 - x)
   D. 1 + x
   Answer: B. It is the liquid mass fraction mf/m = 1 - x. (Key point: Moisture content)

3. Which relation is the starting point of the derivation of the mixture specific volume?
   A. V = mf vg + mg vf
   B. V = m (vf + vg)
   C. V = mf vf + mg vg
   D. V = x vf + (1 - x) vg
   Answer: C. Total volume is the sum of liquid and vapour volumes; dividing by m gives v = (1-x) vf + x vg. (Key point: Starting relation for v)

4. Which is the final expression and its use?
   A. v = vg + x vfg
   B. v = x vf + vg
   C. v = vf + vfg/x
   D. v = vf + x vfg, so x = (v - vf)/vfg
   Answer: D. Rearranging (1-x)vf + x vg gives vf + x(vg - vf). (Key point: Final form)

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