Question

consider the phase diagram of an unknown substance.
segment ab indicates the equilibrium between the solid × and liquid × phases.
segment bc indicates the equilibrium between the solid × and liquid × phases.
segment be indicates the equilibrium between the liquid × and gas × phases.

Explanation:

Step1: Recall phase diagram rules

In a phase diagram, the curves represent equilibrium between two phases. The curve AB (vapor - pressure curve) is between gas (vapor) and liquid? No, wait: AB is the vapor - liquid equilibrium? Wait, no: the three curves are: sublimation (solid - gas), fusion (solid - liquid), vaporization (liquid - gas). Wait, the phase diagram axes: pressure (y) and temperature (x). The curve AB: as temperature increases, pressure increases. This is the vapor - liquid equilibrium (vapor pressure curve), so AB is between liquid and gas? No, wait, no: the correct identification: the three lines:
- Sublimation curve: solid - gas (low pressure, low temp)
- Fusion curve: solid - liquid (slope: if slope is positive, solid is more dense; if negative, liquid is more dense)
- Vaporization curve: liquid - gas (vapor pressure curve, AB here)

Wait, let's re - analyze:

Segment AB: This is the vapor - liquid equilibrium (vapor pressure curve), so it's between liquid and gas? No, wait, no. Wait, the points: A is at low temp and low pressure, B is a point, then AB is the curve where liquid and gas coexist (vapor pressure). Then BC: let's see, the line BC is a steep line, probably the solid - liquid equilibrium (fusion curve). Then BE: wait, BE is the curve from B to E, which is the liquid - gas? No, wait, no. Wait, the correct phase diagram segments:

1. Segment AB: Vapor - Liquid equilibrium (liquid and gas phases coexist). So the first blank (AB) should be gas and liquid? Wait, the original wrong answers: "solid" and "liquid" were wrong. Let's correct:

Segment AB: Equilibrium between gas (vapor) and liquid phases.

Segment BC: Equilibrium between solid and liquid phases (fusion curve, since it's a steep line, probably solid - liquid, as temperature and pressure increase to melt solid).

Segment BE: Wait, BE is the liquid - gas? No, wait, BE is from B to E, which is the liquid - gas? No, wait, the vaporization curve is AB, and the other curve (from B to E) is the liquid - gas? No, maybe I messed up. Wait, let's start over.

In a typical phase diagram:

- The curve between low pressure (y) and low - mid temp (x) (AB) is the vapor - liquid equilibrium (liquid and gas coexist: vapor pressure curve).

- The steep curve (BC) is the solid - liquid equilibrium (fusion curve: solid and liquid coexist).

- The curve from B to E: Wait, no, the three curves are:

- Sublimation (solid - gas): low pressure, low temp (not AB here, since AB is at higher pressure than sublimation usually).

- Fusion (solid - liquid): steep line (BC), as pressure increases, temperature for melting increases (if slope positive, solid is denser).

- Vaporization (liquid - gas): AB, as temperature increases, vapor pressure (pressure of gas in equilibrium with liquid) increases.

- Then the curve from B to E: Wait, maybe BE is the liquid - gas? No, AB is liquid - gas. Wait, maybe the diagram has:

- AB: liquid - gas (vapor pressure)

- BC: solid - liquid (fusion)

- BE: Wait, no, the third curve (from B to E) is liquid - gas? No, maybe the user's diagram has AB as liquid - gas, BC as solid - liquid, and BE as liquid - gas? No, that can't be. Wait, let's correct the original wrong answers:

First segment AB: The correct phases are gas (vapor) and liquid. So the first blank (first box) should be "gas", second "liquid".

Second segment BC: The correct phases are solid and liquid (fusion curve, so solid and liquid coexist). So first box "solid", second "liquid".

Third segment BE: Wait, BE is the liquid - gas? No, AB is liquid - gas. Wait, maybe BE is liquid - gas? No, maybe the curve BE is the liquid - gas, but AB is also liquid - gas? No, that's a mistake. Wait, no, in a phase diagram, the vaporization curve (liquid - gas) is AB, and the other curve (from B to E) is the liquid - gas? No, maybe the diagram has a critical point E, so BE is the liquid - gas up to critical point. Wait, the critical point is where liquid and gas phases become indistinguishable. So BE is the liquid - gas equilibrium (vaporization curve extended to critical point E). So segment BE is between liquid and gas phases.

Wait, let's correct each segment:

1. Segment AB: Equilibrium between gas (vapor) and liquid phases. (Because it's the vapor pressure curve, where liquid and gas coexist at different T and P)

2. Segment BC: Equilibrium between solid and liquid phases. (Because it's the fusion curve, where solid and liquid coexist, steep slope, so as pressure increases, melting temperature increases, meaning solid is more dense)

3. Segment BE: Equilibrium between liquid and gas phases. (Because it's the vaporization curve from B to critical point E, where liquid and gas coexist)

Step1: Correct Segment AB

The original answer had "solid" and "liquid" wrong. In a phase diagram, the curve AB (vapor - pressure curve) is between liquid and gas phases. So the first box (first phase) should be "gas", second "liquid".

Step2: Correct Segment BC

The curve BC is the fusion curve (solid - liquid equilibrium). So the first box (first phase) is "solid", second is "liquid".

Step3: Correct Segment BE

The curve BE is the liquid - gas equilibrium (vaporization curve up to critical point). So the first box (first phase) is "liquid", second is "gas".

Answer:

For Segment AB: gas and liquid (first box: gas, second box: liquid)

For Segment BC: solid and liquid (first box: solid, second box: liquid)

For Segment BE: liquid and gas (first box: liquid, second box: gas)