🔬 Unit 2 – Part A (2-Mark Q&A)

1.What is reduced phase rule?

The reduced phase rule, or condensed phase rule, is a simplified version of the Gibbs phase rule used for a condensed system (solid-liquid equilibrium) where the gas phase is ignored and pressure is held constant.

The mathematical expression is:

• F' = Reduced degrees of freedom
• C = Number of components
• P = Number of phases

2.Give two examples of hybrid composite

Two common examples of hybrid composites are:

1. Carbon Fiber/Glass Fiber: Combines the high strength of carbon with the better impact resistance and lower cost of glass fiber.
2. Aramid Fiber/Carbon Fiber: Combines the exceptional toughness and impact resistance of aramid (like Kevlar) with the high stiffness of carbon fiber.

3.Write the concept of hybrid composite

The concept of a hybrid composite is based on combining two or more different types of reinforcing fibers within a single matrix material.

The core idea is to:

• Synergize Properties: Achieve a balance of properties (e.g., high strength, high stiffness, and high impact resistance) that none of the single-fiber composites could provide alone.
• Optimize Cost: Use a cheaper fiber to replace expensive fiber material in non-critical areas, reducing the final product cost.

This allows the material to be precisely tailored to meet the exact performance requirements of a specific application.

4.State about the requisites of composite materials

The essential requirements (requisites) for composite materials focus on the complementary function of their two main components:

1. Reinforcement (Fibers/Particles): Must have High Strength and High Stiffness (rigidity) to bear the primary loads.
2. Matrix (Binder): Must have Good Adhesion to the reinforcement and sufficient Toughness to hold the fibers in place and transfer stress between them.
3. Final Composite Performance: The resulting material must exhibit a high Strength-to-Weight Ratio, Corrosion Resistance, and Tailorable Properties (e.g., strength in a specific direction).

5.What are the uses of phase diagram

The key uses of a phase diagram are:

• Predicting Alloy Formation: Used to determine whether an eutectic alloy or a solid solution will form when a liquid metal mixture cools.
• Study of Eutectic Alloys: Essential for preparing solders (low melting eutectic alloys) used for joining metals.
• Classification of States: Provides a convenient method for classifying the equilibrium states of a system in terms of phases, components, and degrees of freedom.
• Behavior Prediction: Indicates that different systems with the same degrees of freedom (F) will exhibit similar behavior under changes in temperature, pressure, or concentration.

6.Define component and degree of freedom.

Component (C)
The smallest number of independently variable constituents required to express the composition of every phase in the system.

Degree of Freedom (F)
The minimum number of independent variables (Temperature, Pressure, Concentration) that must be fixed to define the system's state completely.

7.Define phase with an example

A Phase (P) is a homogeneous, physically distinct, and mechanically separable portion of a system, separated from other parts by definite boundaries.

Example: In a system containing Ice(s) ⇌ Water(l) ⇌ Vapour(g), there are three phases: solid ice, liquid water, and gaseous vapor.

8.Write down the composition of lead-silver system

The composition of the lead-silver system at its eutectic point (the lowest melting point) is:

• Lead (Pb): 97.4%
• Silver (Ag): 2.6%

9.What is Pattinson's process?

Pattinson's process is a method used to increase the concentration of silver (Ag) in argentiferous lead (lead containing a small amount of silver).

It works by:

1. Cooling the liquid lead-silver alloy.
2. Pure solid lead (Pb) crystals separate out first.
3. As pure lead is removed, the remaining liquid melt becomes progressively richer in silver until it reaches the eutectic composition (2.6% Ag).

10.Write the mathematical expression of reduced phase rule

The mathematical expression for the reduced phase rule (or condensed phase rule) is:

Where:

• F' = Reduced Degrees of Freedom
• C = Number of Components
• P = Number of Phases

11.What is triple point?

The triple point ('O') is the specific point on a phase diagram where three distinct phases of a substance (typically solid, liquid, and gas/vapor) are simultaneously in thermodynamic equilibrium.

At this point, the system is non-variant (the degrees of freedom, F, is zero), meaning the temperature and pressure are fixed and cannot be independently changed without one of the phases disappearing.

12.Define Components?

Component (C) is defined as, "the smallest number of independently variable constituents, by means of which the composition of each phase can be expressed in the form of a chemical equation."

Essentially, it's the minimum number of chemical entities needed to define the composition of every part (phase) of the system at equilibrium.

13.What do you understand by reduced phase rule?

The reduced phase rule, also known as the condensed phase rule, is a modified form of the Gibbs Phase Rule used to study solid-liquid equilibrium systems.

Its core understanding is:

• It applies to condensed systems where the gas phase is ignored.
• The pressure is assumed to be constant (usually atmospheric pressure), removing it as a variable.
• This simplifies the original Phase Rule (F = C - P + 2) to: F' = C - P + 1

14.What is meant by Eutectic Point

The Eutectic Point ('O') is the specific point on a phase diagram for a mixture (like an alloy) that represents the lowest possible melting temperature for that combination of components.

Characteristics

• Non-Variant State: At the eutectic point, the system is non-variant (degrees of freedom F=0). This means both the composition and the temperature are fixed.
• Three Phases in Equilibrium: At this exact point, three phases coexist in equilibrium: Solid Phase of Component A, Solid Phase of Component B, and The Liquid Phase (melt).
• Simultaneous Solidification: When a liquid of eutectic composition is cooled, it solidifies simultaneously into a fine, intimate mixture of the two solid components, without passing through a partial solidification range.

15.What is condensed Phase rule?

The condensed phase rule, also known as the reduced phase rule, is a modified form of the Gibbs Phase Rule (F = C - P + 2) used to study solid-liquid equilibrium systems.

The rule is based on the assumption that the system is a condensed system where:

• The influence of the gaseous phase is ignored (or negligible).
• Pressure is fixed (usually at atmospheric pressure), removing it as an independent variable.

This reduces the number of independent variables by one, leading to the expression:

16.What is the number of degrees of freedom of a closed system in which CaCO₃(s) is in equilibrium with CaO(s) and CO₂(g)?

The number of degrees of freedom (F) for the given system is 1.

Calculation

The system is: CaCO₃(s) ⇌ CaO(s) + CO₂(g)

1. Phases (P): There are 3 phases (two solids and one gas): CaCO₃(s), CaO(s), and CO₂(g). So, Two P = 3.
2. Components (C): The composition of all 3 phases can be expressed by the minimum of 2 chemical species (e.g., CaO and CO₂). So, C = 2.
3. Phase Rule (F = C - P + 2):
   F = 2 - 3 + 2
   F = 1

The system is univariant, meaning only one variable (either temperature or CO₂ pressure) needs to be fixed to define the equilibrium.

17.What is degree of freedom?

The concept of the Degree of Freedom (F) is derived from the Gibbs Phase Rule and is defined as:

The minimum number of independent variables (Temperature, Pressure, or Concentration) that must be arbitrarily fixed to completely define the system's state of equilibrium.

• F = 0 (Non-variant): The system's state is fixed (e.g., the Triple Point).
• F = 1 (Univariant): Only one variable needs to be set.
• F = 2 (Bivariant): Two variables need to be set.

18.What is the difference between eutectic and triple point?

The eutectic point and the triple point are both important invariant points on phase diagrams, but they differ fundamentally in the number of components and the phases involved.

The key differences are summarized below:

Feature	Eutectic Point	Triple Point
Components (C)	Two or more (C ≥ 2) (e.g., Lead-Silver alloy).	One (C = 1) (e.g., Pure water, pure CO2).
Phases in Equilibrium (P)	Three phases must be present: Liquid and two different solid phases (Solid A + Solid B).	Three phases must be present: Solid, Liquid, and Vapor (Gas).
Phase Rule Application	Uses the Reduced Phase Rule: F' = C - P + 1. For a binary eutectic: F' = 2 - 3 + 1 = 0.	Uses the Full Gibbs Phase Rule: F = C - P + 2. For a pure substance triple point: F = 1 - 3 + 2 = 0.
Variables Ignored	Pressure is usually fixed (ignored); thus, F' is calculated.	Pressure is an active variable; thus, the full F is calculated.
Location on Diagram	Found on a Composition vs. Temperature diagram (binary system).	Found on a Pressure vs. Temperature diagram (pure substance).
Significance	Represents the lowest melting temperature for any mixture of that composition.	Represents the unique temperature and pressure at which all three main states of matter for a pure substance coexist.