Which Of The Following Is An Extensive Property

Let's dive into the world of properties and differentiate between extensive and intensive ones. Understanding this distinction is crucial in various scientific fields, including chemistry, physics, and engineering, as it helps us describe and predict the behavior of matter. To pinpoint which property among a list is extensive, we first need to clarify what exactly defines an extensive property.

Defining Extensive Properties

Extensive properties are those that depend on the amount of matter present. This means that if you increase the quantity of a substance, the value of an extensive property will also increase proportionally. Think of it like this: the more you have of something, the greater the value of its extensive properties.

Here are some key characteristics of extensive properties:

• Additivity: If you combine two identical systems, the value of the extensive property for the combined system will be the sum of the values for the individual systems.
• Dependence on Size or Amount: The value of the property changes directly with the size or amount of the substance being considered.
• Examples: Common examples include mass, volume, length, and total energy.

Common Examples of Extensive Properties

To solidify the concept, let's explore some common examples of extensive properties:

1. Mass: This is perhaps the most straightforward example. If you double the amount of a substance, you double its mass. Mass is the measure of how much "stuff" is in an object.
2. Volume: Volume refers to the amount of space a substance occupies. If you have two cups of water and pour them into a larger container, the total volume of water in the container is the sum of the volumes of the two cups.
3. Length: The length of an object is an extensive property. If you join two identical rods end-to-end, the total length is the sum of the lengths of the individual rods.
4. Energy: Total energy, including kinetic energy, potential energy, and thermal energy, is an extensive property. If you combine two systems, the total energy of the combined system is the sum of the energies of the individual systems.
5. Enthalpy: In thermodynamics, enthalpy is an extensive property that represents the total heat content of a system.
6. Entropy: Entropy, a measure of the disorder or randomness of a system, is also an extensive property.

Extensive vs. Intensive Properties

To truly understand extensive properties, it's helpful to contrast them with intensive properties. Intensive properties do not depend on the amount of matter. These properties are inherent characteristics of the substance itself and remain constant regardless of how much of the substance you have.

Here's a table summarizing the key differences:

Common Examples of Intensive Properties

• Temperature: If you have a cup of coffee at 70°C and pour it into a larger container, the temperature of the coffee remains 70°C. Temperature does not depend on the amount of coffee.
• Pressure: Pressure is the force exerted per unit area. The pressure of a gas in a container does not depend on the size of the container, as long as the gas is uniformly distributed.
• Density: Density is defined as mass per unit volume (ρ = m/V). Density is an intensive property because it is a ratio of two extensive properties (mass and volume). If you double the mass of a substance, you also double its volume, so the ratio (density) remains constant.
• Melting Point: The temperature at which a substance changes from a solid to a liquid is its melting point. The melting point of ice is 0°C, regardless of whether you have a small ice cube or a large block of ice.
• Boiling Point: Similar to the melting point, the boiling point is the temperature at which a substance changes from a liquid to a gas. The boiling point of water is 100°C at standard pressure, regardless of the amount of water.
• Color: The color of a substance is an intensive property. A small sample of copper is the same color as a large copper statue.
• Hardness: Hardness, which measures a material's resistance to localized plastic deformation (e.g., scratching or indentation), is an intensive property.

Identifying Extensive Properties: Practical Examples

Now, let's apply our understanding to some practical examples to identify which properties are extensive.

Example 1:

Consider the following properties:

• Temperature
• Mass
• Density
• Pressure

Which of these is an extensive property?

• Answer: Mass. As we discussed earlier, mass depends on the amount of matter. The other properties (temperature, density, and pressure) are intensive properties.

Example 2:

Which of the following properties of a gas is an extensive property?

• Volume

• Temperature

• Pressure

• Density

• Answer: Volume. The volume of a gas depends on the amount of gas present. The more gas you have, the larger the volume.

Example 3:

Which of the following is an extensive property?

• Boiling Point

• Melting Point

• Energy

• Density

• Answer: Energy. The total energy of a system depends on the amount of substance in the system.

Example 4:

If you have two identical beakers of water, each containing 100 mL of water at 25°C, and you combine them into a single beaker, which of the following properties will double?

• Temperature

• Density

• Volume

• Pressure

• Answer: Volume. When you combine the two beakers of water, the total volume becomes 200 mL, which is double the original volume. The temperature and density of the water will remain the same. Pressure is not relevant in this scenario.

The Importance of Distinguishing Between Extensive and Intensive Properties

Why is it important to distinguish between extensive and intensive properties? The distinction is crucial for several reasons:

1. System Characterization: Understanding whether a property is extensive or intensive helps in characterizing and describing a system accurately. It allows scientists and engineers to predict how the system will behave under different conditions.
2. Scaling and Design: In engineering design, it is essential to know how properties will scale with the size of the system. Extensive properties are crucial in scaling calculations. For example, when designing a chemical reactor, engineers need to consider the total mass and volume of reactants.
3. Thermodynamic Analysis: In thermodynamics, the distinction between extensive and intensive properties is fundamental. Thermodynamic equations often relate extensive properties (such as energy and enthalpy) to intensive properties (such as temperature and pressure).
4. Material Science: In material science, understanding the nature of material properties is essential for selecting the right materials for specific applications. For example, the density of a material (an intensive property) is a key factor in determining its suitability for structural applications.
5. Chemical Reactions: When studying chemical reactions, it is important to know how the amounts of reactants and products affect the overall process. Extensive properties like mass and volume play a critical role in stoichiometric calculations.

Mathematical Representation

Mathematically, the relationship between extensive and intensive properties can be expressed as follows:

Let's say we have a system with an extensive property E and we divide the system into n identical subsystems. If e is the value of the extensive property for each subsystem, then:

E = n * e

For example, if we have a container of gas with a volume V and we divide the container into two equal parts, each part will have a volume of V/2.

Intensive properties, on the other hand, remain constant when the system is divided. If I is an intensive property of the system, then each subsystem will also have the same value I.

Common Misconceptions

Here are some common misconceptions about extensive and intensive properties:

• Misconception 1: "Extensive properties are always easy to measure." This is not necessarily true. While some extensive properties like mass and volume are relatively easy to measure, others, such as total energy, can be challenging to determine accurately.
• Misconception 2: "Intensive properties are always more important than extensive properties." The importance of a property depends on the context. In some cases, intensive properties are more relevant, while in others, extensive properties are more critical. For example, when designing a pressure vessel, the tensile strength of the material (an intensive property) is crucial. However, the total mass of the vessel (an extensive property) is also important for structural support considerations.
• Misconception 3: "Density is an extensive property because it involves mass and volume." Density is defined as mass per unit volume (ρ = m/V). Although it is calculated using two extensive properties, density itself is an intensive property because it is a ratio. When you increase the amount of a substance, both its mass and volume increase proportionally, so the ratio (density) remains constant.

Examples in Everyday Life

The concepts of extensive and intensive properties are not just theoretical; they appear in our everyday lives.

• Cooking: When cooking, the amount of ingredients you use (mass) is an extensive property that affects the final outcome of the dish. The temperature at which you bake a cake (an intensive property) also plays a critical role.
• Gardening: The amount of soil you need for a garden bed (volume) is an extensive property. The pH of the soil (an intensive property) affects the growth of plants.
• Home Heating: The amount of energy needed to heat a house (an extensive property) depends on the size of the house. The temperature you set on the thermostat (an intensive property) determines how warm the house will be.
• Driving: The amount of gasoline in your car's tank (volume) is an extensive property. The pressure in your car's tires (an intensive property) affects the car's handling and fuel efficiency.

Advanced Concepts

For those interested in delving deeper into the topic, here are some advanced concepts related to extensive and intensive properties:

• Chemical Potential: In thermodynamics, chemical potential is an intensive property that describes how the Gibbs free energy of a system changes with the addition or removal of particles.
• Specific Properties: Specific properties are intensive properties obtained by dividing an extensive property by mass. For example, specific volume is volume divided by mass (v = V/m), and specific energy is energy divided by mass (e = E/m).
• Molar Properties: Molar properties are intensive properties obtained by dividing an extensive property by the amount of substance (in moles). For example, molar volume is volume divided by the number of moles (Vm = V/n).
• State Functions: In thermodynamics, state functions are properties that depend only on the current state of the system and not on the path taken to reach that state. State functions can be either extensive (e.g., energy, enthalpy, entropy) or intensive (e.g., temperature, pressure).

Conclusion

In summary, the distinction between extensive and intensive properties is fundamental in science and engineering. Extensive properties depend on the amount of matter present, while intensive properties do not. Understanding this difference is crucial for characterizing systems, making predictions, and designing processes. Mass, volume, energy, and enthalpy are common examples of extensive properties, while temperature, pressure, and density are common examples of intensive properties. By mastering these concepts, you will be better equipped to analyze and solve problems in various scientific and engineering disciplines.