14.2.1. Definition of Properties

Extensive property is considered proportional to the amount of mass. When you apply extensive properties, it means the properties which are proportional to the amount of mass. As mass increases, the extensive properties increase. If mass decreases, the extensive property decreases. For example, when considering mass conservation, momentum conservation, and energy conservation, the relationship is clear; mass (m) is the conservation part for momentum and energy.

Extensive properties are those that depend on the amount of material present in a system. For example, if you take a block of ice, the mass of the ice is an extensive property. If you cut the ice block in half, the mass reduces, demonstrating that extensive properties change with the size of the system. Mathematically, extensive properties can be represented as B, which changes with mass (m) of the system, following the relationship dB/dm.

Think of extensive properties like a buffet at a restaurant. The amount of food (mass) on your plate is an extensive property. If you pile more food on your plate, the total quantity increases. If you eat some off the plate, the quantity decreases. Just like that, total mass, momentum, and energy change according to your 'portion size' or mass.

Intensive properties are independent of mass, which means that these properties remain constant regardless of the amount of material present. For example, temperature or pressure can be considered as intensive properties. In the context of energy conservation, the extensive property can be identified as energy, while the intensive property is specific energy, denoted as e, which is energy per unit mass.

Intensive properties do not change when the system size changes. For instance, if you have a pot of boiling water and you remove some water, the temperature of the water (an intensive property) remains the same. This illustrates that while extensive properties depend on the size or mass of the material, intensive properties are characteristics irrespective of the amount of material. The relationship can be identified mathematically ase = B/m.

Think of intensive properties as the color of a dye. Whether you have a small drop or a large jar full of dye, the hue remains the same. Just like that, properties like temperature don't change with how much material you have—if it's 100 degrees Celsius, it stays 100 degrees regardless of whether you have a cup of water or an entire bathtub!

The relationship between extensive property (B) and intensive property (b) is simple: dB/dm gives the ratio of extensive to specific coverage of intensive property. This shows how the two properties relate to one another; while extensive properties can be summed or divided, intensive properties provide a normalized measure per unit mass which is consistent across different amounts.

This relationship highlights the differences in how these properties function. As outlined earlier, extensive properties add together based on mass, while intensive properties always remain consistent, providing a fundamental basis for their ratio expressed as dB/dm. Understanding this relationship is key in fluid mechanics, where you may need to switch between these properties depending on the calculations required.

Imagine you are measuring sports performance—like a runner's speed. The total distance run is akin to extensive properties (B), while the speed (distance per time) represents an intensive property (b). Speed remains unchanged regardless of how far the runner goes; one can think of a speedometer showing consistent numbers irrespective of the total distance traveled.

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