Intensive and Extensive Properties

Thermodynamics is the study of energy, heat, and their transformations in physical systems. A fundamental concept in thermodynamics is the classification of properties into intensive and extensive categories. Understanding these properties is crucial because they determine how we analyze systems, perform calculations, and predict physical behavior.

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1. Introduction to Thermodynamic Properties

A thermodynamic property is any measurable quantity that describes the state of a system. These properties can be macroscopic, like pressure, volume, or temperature, or microscopic, like molecular energy. Thermodynamic properties help us:

• Define the state of a system
• Describe changes in the system during thermodynamic processes
• Apply laws of thermodynamics effectively

Thermodynamic properties are broadly classified into intensive and extensive properties.

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2. Definition of Intensive and Extensive Properties

2.1 Extensive Properties

Definition: Extensive properties are those that depend on the size or mass of the system. If the system is divided into two equal parts, the extensive property also divides proportionally.

• Dependence: Total quantity increases or decreases with the amount of matter.
• Examples: Mass, volume, total energy, total charge, total enthalpy.

Mathematical Representation:

If a system is divided into two equal parts: Property of part 1+Property of part 2=Property of whole system\text{Property of part 1} + \text{Property of part 2} = \text{Property of whole system}Property of part 1+Property of part 2=Property of whole system

Example:

• A container has 2 liters of water (extensive property: volume). If you split it into two 1-liter containers, each has 1 liter, and the total is still 2 liters.

2.2 Intensive Properties

Definition: Intensive properties are those that do not depend on the size or mass of the system. They remain the same whether the system is large or small.

• Independence: Value is the same for a part or the whole system.
• Examples: Temperature, pressure, density, refractive index, color, specific volume, specific energy.

Mathematical Representation:

Intensive properties are ratios of extensive properties. For example: Density(ρ)=MassVolume\text{Density} (\rho) = \frac{\text{Mass}}{\text{Volume}}Density(ρ)=VolumeMass​

Here, mass and volume are extensive, but density is intensive.

Example:

• A 2-liter container of water at 25°C has the same temperature if split into two 1-liter containers.

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3. Importance of Distinguishing Between Intensive and Extensive Properties

The distinction between intensive and extensive properties is crucial in:

1. Thermodynamic Calculations: Intensive properties are used to define the state of a system, while extensive properties quantify the total energy or matter.
2. Scaling Systems: Extensive properties scale with system size; intensive properties remain unchanged.
3. Design of Systems: Engineers use intensive properties for uniformity in processes (e.g., temperature and pressure) and extensive properties for sizing systems (e.g., fuel mass, heat content).

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4. Examples of Extensive Properties

Here is a list of common extensive properties:

1. Mass (m) – Total amount of matter in the system.
2. Volume (V) – Space occupied by the system.
3. Total Internal Energy (U) – Sum of kinetic and potential energies of all particles.
4. Enthalpy (H) – Total heat content at constant pressure.
5. Entropy (S) – Total measure of disorder or randomness.
6. Electric charge (Q) – Total charge in a system.
7. Number of particles (N) – Total count of molecules or atoms.

Key Feature: Doubling the system doubles the extensive property.

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5. Examples of Intensive Properties

Here is a list of common intensive properties:

1. Temperature (T) – Measure of average kinetic energy of particles.
2. Pressure (P) – Force per unit area exerted by particles.
3. Density (ρ\rhoρ) – Mass per unit volume.
4. Specific volume (vvv) – Volume per unit mass.
5. Specific energy – Energy per unit mass.
6. Viscosity (η\etaη) – Fluid’s resistance to flow.
7. Surface tension (γ\gammaγ) – Energy per unit area of a liquid surface.

Key Feature: Splitting the system does not affect the intensive property.

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6. Relationship Between Intensive and Extensive Properties

Many intensive properties are derived from ratios of extensive properties. This relationship is crucial in thermodynamics and engineering: Intensive Property=Extensive PropertyMass or Volume\text{Intensive Property} = \frac{\text{Extensive Property}}{\text{Mass or Volume}}Intensive Property=Mass or VolumeExtensive Property​

Examples:

1. Density:

ρ=mV\rho = \frac{m}{V}ρ=Vm​

• Mass and volume are extensive; density is intensive.

2. Specific internal energy:

u=Umu = \frac{U}{m}u=mU​

• Total internal energy (extensive) divided by mass gives specific internal energy (intensive).

3. Specific enthalpy:

h=Hmh = \frac{H}{m}h=mH​

• Enthalpy per unit mass is intensive.

4. Specific entropy:

s=Sms = \frac{S}{m}s=mS​

• Entropy per unit mass is intensive.

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7. Examples in Daily Life

Understanding intensive and extensive properties is not limited to textbooks; they appear in everyday experiences:

1. Cooking:
   • Heat content (extensive) depends on the quantity of food.
   • Temperature (intensive) determines cooking rate.
2. Water in a Tank:
   • Volume of water (extensive) changes if the tank size changes.
   • Pressure at the bottom (intensive) depends on depth, not tank size.
3. Air Conditioning:
   • Energy supplied (extensive) varies with room size.
   • Temperature (intensive) is controlled for comfort.
4. Fuel in Cars:
   • Mass of fuel (extensive) affects range.
   • Energy density (intensive) remains constant for the fuel type.

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8. Extensive and Intensive Properties in Thermodynamic Processes

Thermodynamic analysis often involves tracking properties during processes:

1. Isothermal Process (constant temperature):
   • Temperature (intensive) remains constant.
   • Internal energy (extensive) may change if the system exchanges heat or work.
2. Adiabatic Process (no heat transfer):
   • Entropy per unit mass (intensive) may remain constant for reversible adiabatic processes.
   • Total internal energy (extensive) changes as work is done.
3. Isochoric Process (constant volume):
   • Volume (extensive) remains constant.
   • Pressure (intensive) changes with heat addition.

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9. Mathematical Treatment

Let a system have an extensive property XXX and a mass mmm. Its corresponding intensive property xxx is: x=Xmx = \frac{X}{m}x=mX​

If the system is split into two parts:

• Extensive: X=X1+X2X = X_1 + X_2X=X1​+X2​
• Intensive: x=x1=x2x = x_1 = x_2x=x1​=x2​

Example:

• Total internal energy UUU = 1000 J (extensive) in a 2 kg system.
• Specific internal energy u=U/m=500 J/kgu = U/m = 500\text{ J/kg}u=U/m=500 J/kg (intensive).
• Splitting into 1 kg parts:
  • U1=U2=500 JU_1 = U_2 = 500\text{ J}U1​=U2​=500 J (extensive)
  • u1=u2=500 J/kgu_1 = u_2 = 500\text{ J/kg}u1​=u2​=500 J/kg (intensive)

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10. Role in Thermodynamic Equations

Thermodynamic equations often mix intensive and extensive properties. Correct usage ensures accuracy in calculations:

1. First Law of Thermodynamics:

ΔU=Q−W\Delta U = Q – WΔU=Q−W

• UUU (extensive) depends on system size.
• QQQ (extensive) and WWW (extensive) scale with system size.

2. Gibbs Free Energy:

G=H−TSG = H – TSG=H−TS

• HHH and SSS are extensive.
• Temperature TTT is intensive.

3. Chemical Potential:

μ=(∂G∂n)T,P\mu = \left( \frac{\partial G}{\partial n} \right)_{T,P}μ=(∂n∂G​)T,P​

• μ\muμ is intensive.
• GGG (extensive) divided by number of moles gives chemical potential.

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11. Applications in Engineering and Science

Understanding intensive and extensive properties is crucial in:

1. Chemical Engineering:
   • Designing reactors requires mass (extensive) and concentration (intensive) data.
2. Mechanical Engineering:
   • Energy and work calculations rely on extensive properties.
   • Pressure and temperature controls are intensive for safety and efficiency.
3. Material Science:
   • Density and melting point (intensive) define material selection.
   • Mass and volume (extensive) affect structural design.
4. Meteorology:
   • Temperature and pressure (intensive) determine weather conditions.
   • Total heat content (extensive) affects climate modeling.

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12. Summary Table

Property Type	Definition	Depends on System Size?	Examples
Extensive	Depends on system size	Yes	Mass, Volume, Energy, Enthalpy, Entropy
Intensive	Independent of system size	No	Temperature, Pressure, Density, Specific Energy, Chemical Potential