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# Extensive Property

Dive into the world of engineering thermodynamics as you explore the concept of Extensive Property. This critical aspect underpins many fundamental principles and calculations within the wide-ranging field of engineering. Grasp the meaning, formula, and stark contrasts between extensive and intensive properties, leading to a better understanding of their distinctive roles. You'll gain deep insights through meticulously chosen examples and real-world applications that encapsulate the importance of Extensive Property in engineering. This critical knowledge will equip you to address challenging engineering problems effectively.

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## Understanding Extensive Property in Engineering Thermodynamics

In the fascinating field of engineering thermodynamics, you will encounter extensive properties. But what exactly is an extensive property? To put it simply, these are properties of a system that change according to the amount of matter present.

An extensive property can be defined as one which depends on the quantity of matter in the system. Therefore, if the system is doubled, the property also doubles. Examples of extensive properties include mass, energy, and volume.

### Breakdown of the Extensive Property Meaning

Understanding extensive properties requires some knowledge of system properties in thermodynamics. In engineering thermodynamics, properties can be categorised into extensive and intensive. While Extensive properties depend on the amount of material, intensive properties remain the same regardless of the system size.

• Extensive Properties: Energy, Volume, Mass
• Intensive Properties: Pressure, Temperature

#### Relation Between Extensive Property and System Size

It's essential to understand the direct relationship between an extensive property and the size of the system. As the system size increases, so does the value of the extensive property.

For instance, if you have a gas in a container, the mass of the gas (an extensive property) will linearly increase as you add more gas to the container, thus increasing the system's size.

### Demystifying the Extensive Property Formula

In engineering, you may often need to use equations that involve extensive properties. The formula for an extensive property relies on the property's direct proportionality to the system's size. $E = kN$ In this formula, $$E$$ stands for the extensive property, $$k$$ is a proportionality constant, and $$N$$ is the system's measure (like volume for liquid or number of particles for gases).

#### Practical Usage of Extensive Property Formula in Calculations

Let's consider an example - apply the above formula in the calculation of extensive property such as energy. Let's assume we have a system with 500 particles, and each particle contributes 2 units of energy. In this case, the total energy $$E$$ (an extensive property) would be:

$E=2\times500 = 1000 \text{ units}.$

However, if the number of particles is increased by a factor of 2, the total energy $$E$$ would also increase by the same factor.

$E=2\times1000 = 2000 \text{ units}.$

As can be seen, the extensive property (Energy) increases as the size of the system (Number of particles) increases.

Interestingly, the concept of extensive property has been applied in various scientific and engineering fields, including computational elements of programming languages, where certain attributes can scale or expand similarly.

## Examples of Extensive Property in Thermodynamics

In thermodynamics, extensive properties play a crucial role. The most typical examples of extensive properties include mass, volume, and energy. The unique trait of these properties is that their magnitude is directly influenced by the quantity or size of the system under consideration.

### Detailed Examination of Extensive Property Examples

When studying thermodynamics, especially in engineering, you can come across various examples of extensive properties. Let's consider the examples of mass, volume, and energy to understand the concept better.

Mass: It is one of the most simple-to-understand extensive properties. The mass of an object is directly dependent on the amount of matter present in the object. Thus, if you were to double the quantity of matter, the mass would also double.

Volume: Volume, like mass, is another example of an extensive property. The volume of a substance depends on the amount of the substance you have. Therefore, if you double the quantity of a substance, the volume doubles as well.

Energy: Energy in a system is also an extensive property. It depends on the mass and the speed at which the bodies in the system are moving. More the mass or more the movement, more will be the energy and vice versa.

#### Contrast of Extensive and Intensive Properties through Examples

Understanding the distinction between extensive and intensive properties can provide deeper insights into their significance in thermodynamics. As you already know, extensive properties such as mass, volume, and energy increase directly with the size of the system. Conversely, intensive properties, like temperature and pressure, remain the same regardless of the size of the system.

Consider for example a beaker of water at a constant temperature. The quantity of water (mass and volume - extensive properties) will change if you add or remove water from the beaker. However, the temperature reading (an intensive property) remains the same irrespective of the amount of water in the beaker. It is not affected by the change in the system's size.

### Real-World Applications of Extensive Property

Extensive properties hold practical applications in numerous real-world scenarios, especially within industries and sectors that manipulate materials or substances. Some of these applications are shared below:

Chemical Engineering: In chemical engineering design processes, understanding the extensive properties of substances is critical to controlling the design and operation of systems. For example, predicting how much heat (an extensive property) is required for a reaction can contribute to optimising energy usage.

Civil Engineering: In civil engineering, a familiar example is cement mixing — understanding that the volume (an extensive property) of cement needed is solely based on the size of the construction project.

Environmental Engineering: Extensive properties also have numerous practical applications in environmental engineering, including waste and pollution management. For example, understanding the specific volume of pollutants (an extensive property) can assist in developing effective strategies for their removal or reduction.

Material Science: In material science, the specific energy (an extensive property) of materials aids in determining their suitability for various applications. For example, high energy materials are ideal for tasks requiring significant power, such as jet propulsion.

In all these cases, the concept of extensive properties is vital to optimise processes and achieve desired outcomes.

## Comparative Study of Extensive and Intensive Property

In the broad spectrum of thermodynamics within engineering, properties of a system are categorically divided into extensive and intensive based on their dependency or lack of dependency on the amount of material present. Although it may seem daunting at first, understanding the clear line that separates extensive properties from intensive properties can help elucidate many concepts inherent in thermodynamics.

### Dissimilarity Between Intensive and Extensive Property

Even though both intensive and extensive properties are inherent characteristics of a system, the primary difference between lies in the dependency on the system size. Extensive properties are directly proportional to the system size while intensive properties remain constant, irrespective of the size of the system. It's important to note that any ratio of two extensive properties gives rise to an intensive property. This can be represented by the formula:

$I = \frac{E_1}{E_2}$

Where $$I$$ is the intensive property and $$E_1$$ and $$E_2$$ are extensive properties. From the equation, one can infer that the value of an intensive property is dimensionless as it's a ratio of two similar dimensions. This also implies that an intensive property doesn't have a physical dimension.

#### Specific Instances Highlighting Differences of Intensive and Extensive Property

A more concrete understanding of the differences can be obtained by considering specific instances. When you heat water in a container, the temperature increase is the same regardless of the quantity of water - this represents an intensive property. In contrast, the total heat content of the water - which depends upon both its mass and temperature - is an extensive property. Another common example is pressure. No matter how much of the fluid you have, the pressure at a particular depth of the fluid remains constant. However, the weight of the fluid, which depends directly upon the volume and hence the amount of fluid, is an extensive property.

 Intensive Property Extensive Property Temperature Heat Content Pressure Weight

### Significance of Distinguishing Between Intensive and Extensive Property

Understanding the difference between intensive and extensive properties is of considerable importance in engineering and scientific computations as it affects how systems react when they're split or combined. For instance, the total energy of a system - a quintessential extensive property - can give decisive insights into its combined behaviour. However, when you're more interested in the individual behaviour of particles, intensive properties like temperature and pressure become more relevant.

Furthermore, it shapes our perception and the applied methodology in problems involving varied system sizes. The amount of heat needed to raise the temperature of a substance (an intensive property) by a certain amount is proportional to the mass of the substance (an extensive property). This understanding is critical for engineers when dealing with large-scale chemical reactors in industry or small lab-scale experiments. So in essence, distinguishing between intensive and extensive properties helps engineers and scientists ensure that their calculations and predictions are both accurate and relevant.

## Extensive Property Applications in Engineering

The concept of extensive property, core to fundamental thermodynamics, is applied accross many disciplines within engineering, including but not limited to, mechanical, civil, and chemical engineering. It's application in materials processing, resource management, and efficiency audits, among others, underscores its practical relevance to real-life problems.

### Utilising Extensive Property in Real-Life Engineering Problems

An extensive property is a physical quantity whose value is directly proportional to the size or extent of the system it represents. Prominent examples are mass, volume, and total energy.

In chemical engineering, understanding extensive properties of substances is crucial for designing and optimising chemical reactors and separation processes. For instance, the total amount of heat (an extensive property) required to effect a chemical reaction is fundamental in process design and energy management. The mass of reactants and volume of a reactor, both extensive properties, are pertinent to controlling the reaction rates and yield.

In the realm of mechanical engineering, extensive properties play a pivotal role in thermodynamic systems. For example, the total energy of a system, an extensive property, is a determining factor in the performance and efficiency of heat engines and refrigeration systems. Similarly, the volumetric capacity of fluid containers and conduits, an extensive property, impacts the design of piping and pumping systems.

Civil and environmental engineering professionals also utilise the concept of extensive properties in their work. In waste management and pollution control, for instance, the total volume of waste or pollutant is an important factor in determining the appropriate methods and equipment for their disposal or treatment. In civil construction projects, the total volume of materials like concrete and steel, are critical in project estimation and management.

Materials engineers use the extensive property of materials in determining their suitability for applications. For example, the energy levels of certain materials, an extensive property, helps them understand what types of tasks they are suitable for.

#### Deep Dive into the Practical Applications of Extensive Property

Let's take the example of a steam power plant. The functionality of the plant depends on the conversion of thermal energy into mechanical work, a task largely dependent on the properties of steam used. The total internal energy and enthalpy of steam, both extensive properties, directly influence the efficiency of energy conversion. Changing the mass of steam (another extensive property) would effect these extensive properties and therefore alter plant performance.

Another interesting application of extensive properties can be found in the field of material science. Take, for instance, lithium-ion batteries. The total electric charge a battery can deliver, an extensive property, depends on the total mass of active materials in the electrodes. Charging and discharging behaviours of the battery, although dictated by intensive properties like potential difference (voltage), are also greatly influenced by the battery's extensive properties.

In chemical engineering, consider a distillation column used to separate a mixture of liquids. The dimensions of the column (an extensive property), the total mass and composition of the feedstock (extensive properties), and the total heat supplied to the column (an extensive property), will dictate the quality and quantity of the distillate and bottoms products.

Finally, consider road construction in civil engineering. The design and cost of a road depends on the total volume of asphalt required, which is an extensive property. Changes in project specifications, such as road length and thickness, will alter this volume and thereby affect project cost and timeline."

From thermodynamics to material science, extensive properties offer a robust and insightful tool for understanding and manipulating the world around us. While these examples provide a glimpse into the uses of extensive properties in engineering, they only scratch the surface of the myriad of ways these concepts underpin our modern infrastructure and technology.

## Extensive Property - Key takeaways

• The concept of Extensive Property depends on the quantity of matter in a system. If the quantity doubles, the property also doubles. Examples include mass, energy, and volume.
• Extensive properties are categorised differently from Intensive properties where Extensive properties depend on the amount of material present and Intensive properties remain the same regardless of the system size.
• There's a direct relationship between an Extensive Property and the size of the system. As the system size increases, so does the value of the Extensive Property.
• The Extensive Property formula involves the property's direct proportionality to the system's size, characterised by $$E = kN$$, where $$E$$ stands for the Extensive Property, $$k$$ is a proportionality constant, and $$N$$ is the system's measure.
• The idea of Extensive Property plays a significant role in many scientific and technical fields. In thermodynamics, mass, volume, and energy are typical examples of Extensive Property, and their magnitude is directly influenced by the size or quantity of the system under consideration.

#### Flashcards in Extensive Property 51

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What is an extensive property?
An extensive property in engineering is a property that changes when the size of the system changes. Examples include mass, volume and total charge – they depend on the quantity of material in the system.
Is temperature an extensive property?
No, temperature is not an extensive property. It is an intensive property, meaning it doesn't change with the amount of substance involved. Extensive properties, like mass or volume, do vary with the quantity of substance.
What are intensive and extensive properties in thermodynamics? Please write in UK English.
Intensive properties in thermodynamics are those that do not depend on the quantity of a substance, like temperature or pressure. Extensive properties, on the other hand, do depend on the quantity of material, such as mass and volume.
Is entropy an extensive property?
Yes, entropy is an extensive property. This means that its magnitude is directly related to the amount of material in the system. If the system is divided, the total entropy also divides.
What is an extensive physical property? Please write in UK English.
An extensive physical property is a property that changes when the amount of matter in a substance changes. Examples include mass, volume, and total charge. These properties are dependent on the amount of substance present.

## Test your knowledge with multiple choice flashcards

Why is distinguishing between intensive and extensive properties important in engineering and scientific computations?

How do extensive properties contribute to the field of material science, specifically with regards to lithium-ion batteries?

Can you give an example demonstrating the relationship between an extensive property and system size?

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