Question

f a mixture has a volume of 1,551 cubic cm and a mass of 120 grams

and the vapor portion has a specific volume of 0.15 cubic meters per kg

and the liquid portion has a specific volume of 0.0007 cubic meters per kg.

What is the quality of the mixture?

Answer 1

Theory: We need to balance the the total specific volume to individual liquid and vapor specific volume.

Quality in a mixture is the vapor fraction in the mixture.

Solution:

Step 1: Total volume of system = 1551 cm3 = 1551/10⁶ m3 = 0.001551 m3

Total mass of system = 120 gm = 0.12 Kg

so Specific volume of system = V = total volume/total mass = 0.001551/0.12 = 0.012925 m3/kg

Step 2: Specific volume of vapor = Vv = 0.15 m3/Kg

Specific volume of liquid = Vl = 0.0007 m3/Kg

Lets assume quality of the mixture is X

then doing the volume balance:

V = Vv*X + (1-X)*Vl

0.012925 = 0.15X + (1-X)*0.0007

or X = 0.08188 or 8.188%