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Quality, moisture content, specific volume of mixture

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.

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

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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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