Quality needed to pass through critical point (thermodynamics)

[General_Sax]

Homework Statement

A rigid tank contains 1 kg of saturated liquid and saturated vapor mixture at 400
kPa. What quality (x1) do you need if you want the P-v diagram to pass through
the critical point? Use steam tables to answer this question.

Homework Equations

x = quality = [mass(gas)]/[mass(gas + liquid)]

critical specific volume = 0.003155 [m^3/kg]

The Attempt at a Solution

Now to me the question seems meaningless, because the rigid tank will contain a constant volume and a constant mass, so it will have a constant specific volume.

The quality upon the approach to the critical point will vary with pressure... so really you just need to ensure that the tank has a specific volume of 0.003155 [m^3/kg] and the the P-v diagram will pass through the critical point.

Have I overlooked something?

 

[stacks3]

Try the equation v=vf + x*vfg for saturated liquid-vapor mixtures, you can use the saturation tables to find vf and vfg