Unary Diagrams

1
Unary Diagrams

• Tutorial by
• Doug Legel

2
Unary System

• What is a unary system?
• One Component
• At least three phase

3
How to Draw unary diagrams

• 1. Read the conditions
• 2. Plot boundary lines
• 3. Label regions
• 4. Check conditions

4
Example Problem 1

• You have a 3 phase system.
• The solid is more dense than the Liquid.
• The solid sublimes, and melts.

5
Example Problem 1

• The Solid is more dense than the Liquid
• What does this mean?
• It means that by increasing pressure at a
  constant temperature, the liquid will turn into a
  solid.

6
Example Problem 1

• The solid sublimes, and melts.
• What does this mean?
• It means that the Solid region needs to share a
  boundary line with both the Vapor, and Liquid
  regions.

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Example 1

• First draw in the Vapor boundary line

Liquid
Solid

• Next draw the Solid-Liquid boundary line

Pressure

• Next Label the Regions

Vapor
Temperature
8
Example 1

• Now check to make sure your diagram meets the
  conditions.

Liquid
Solid
2
1
Pressure

• Are there 3 phases?

Vapor
3
Temperature
9
Example 1

• Is the Solid more dense than the Liquid?

Liquid
Solid

• To check, draw an iso-thermal line

Pressure

• Notice that as pressure is increased along the
  isotherm, the Liquid turns into Solid. So the
  Solid is more dense.

Vapor
Temperature
10
Example Problem 2

• You have a single component, 3 phase system.
• The solid is less dense than the Liquid
• The solid sublimes, and melts

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Example 2

• First draw in the vapor boundary line

Liquid
Solid

• Next draw the Solid Liquid boundary line

Pressure

• Next Label the Regions

Vapor
Temperature
12
Example 2

• Is the Liquid more dense than the Solid?

Liquid
Solid

• Check with an iso-thermal line

Pressure

• Notice as pressure is increased along the
  isotherm, the Solid turns into Liquid. So the
  Liquid is more dense.

Vapor
Temperature
13
Example Problem 3

• You have a 3 phase system.
• The solid melts but does not sublime

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Example Problem 3

• The solid melts but does not sublime
• What does this mean?
• It means that the Solid region does not share a
  boundary line with the Vapor region

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Example 3

• First draw in the vapor boundary line

Liquid
Solid

• Next draw the Solid Liquid boundary line

Pressure

• Next Label the Regions

Vapor
Temperature
16
Example Problem 4

• You have a 4 phase system.
• Solid 1 and 2 are more dense than the liquid
• The Solid 1 sublimes, and melts
• Solid 2 is more dense than Solid 1
• Solid 2 melts but does not sublime

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Example 4

• First draw in the vapor boundary line

Solid 2
Liquid
Solid 1

• Next draw the Solid Liquid boundary line

Pressure

• Next draw the Solid-Solid boundary line

Vapor

• Next Label the Regions

Temperature
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Example 4

• Now check to make sure your diagram meets the
  conditions

Solid 2
Liquid
2
Solid 1
3
1
Pressure

• Are there 4 phases?

Vapor
4
Temperature
19
Example 4

• Are the Solids more dense than the Liquid?

Solid 2
Liquid
Solid 1

• Check with iso-thermal lines

Pressure

• Notice that as pressure is increased along the
  isotherm, the Liquid turns into Solid 1 and Solid
  2. So the solids are more dense.

Vapor
Temperature
20
Example 4

• Is Solid 1 more dense than Solid 2?

Solid 2
Liquid
Solid 1

• Check with another iso-thermal line

Pressure

• Notice that as pressure is increased along the
  isotherm, Solid 1 turns into Solid 2. So Solid 1
  is more dense.

Vapor
Temperature
21
Summary

• Through the 4 examples, many situations were
  examined.
• Combining the situations given in the examples
  will allow you to solve any unary diagram
  problem.
• If you understand the examples, it is relatively
  easy to dissect a problem and construct a Unary
  diagram.