14.2.2. Extensive vs Intensive Properties

The extensive property which is considered as proportional to the amount of mass. When you apply extensive properties, that means you are the properties which are proportional to the amount of mass. That means, as mass increases you will have extensive properties going to increase.

Extensive properties are quantities that change when the amount of matter or the mass of a system changes. For example, if you have a larger amount of a substance, properties like mass, volume, and total energy will increase proportionally. Conversely, if you reduce the amount of substance, these properties will decrease accordingly. Thus, extensive properties directly relate to the total mass of a system.

Think about how a bag of flour behaves. If you have a 2 kg bag, it has a certain mass, volume, and energy associated with it. If you increase the bag to 4 kg, all these extensive properties double. In simple terms, extensive properties are like the total weight of groceries in your shopping cart; if you buy more groceries, the weight increases.

But when you look at the intensive properties, that means it is independent of mass, that means, which is denoted as . So, if you look it that way, there are two properties, extensive property and intensive property. In intensive property independent to mass or , per unit mass what we are talking about.

Intensive properties are characteristics of a material that do not change regardless of the amount of substance present. These properties remain constant whether you have a small sample or a large one. Examples of intensive properties include density, temperature, and pressure. For instance, if you have a cup of water or a swimming pool full of water, the temperature of the water remains the same irrespective of the quantity.

Imagine tasting sugar in water. Whether you dissolve one spoonful of sugar in a cup or dissolve a whole bag in a large vat of water, the concentration (an intensive property) remains the same until saturation is reached. This illustrates the nature of intensive properties—you can always find the same flavor profile regardless of the size of your sample.

We define the difference between extensive property and intensive property. Extensive property we define as B, intensive property we define as b. They have the relationship, simple relation like this, mathematically dB by dm.

The relationship between extensive and intensive properties is fundamental in thermodynamics and fluid mechanics. For instance, if we denote the extensive property as B (like energy) and the intensive property as b (like specific energy), the relationship can be expressed mathematically. The ratio of the extensive property to mass gives the equivalent intensive property. Hence, we can understand that 'b = B/m', meaning specific energy is dependent on total energy divided by mass.

Consider a pizza. The total energy (extensive property) in the pizza is how much energy is in the whole pizza (B). But if you take one slice from that pizza, the energy per slice represents the specific energy (intensive property). As you divide the pizza, the total energy decreases but the energy per slice (intensive property) remains constant if the slices are of equal size.

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