Extensive Quantity vs. Intensive Quantity

Attribute	Extensive Quantity	Intensive Quantity
Definition	Depends on the size or amount of the substance	Does not depend on the size or amount of the substance
Examples	Mass, volume, energy	Density, temperature, pressure
Units	kg, L, J	kg/m^3, K, Pa
Formula	Extensive Quantity = Intensive Quantity x Size/Amount	Intensive Quantity = Extensive Quantity / Size/Amount

Definition

Extensive quantity and intensive quantity are two fundamental concepts in the field of physics and mathematics. Extensive quantity refers to a physical quantity that depends on the size or extent of a system, such as mass, volume, or energy. In contrast, intensive quantity is a physical quantity that does not depend on the size or extent of a system, such as temperature, pressure, or density.

Characteristics

Extensive quantities are additive, meaning that the total value of the quantity for a system is the sum of the values for its individual parts. For example, the total mass of a system is the sum of the masses of its components. Intensive quantities, on the other hand, are not additive and are independent of the size of the system. This means that the value of an intensive quantity remains the same regardless of the size of the system.

Units

The units of measurement for extensive quantities are typically extensive units, such as kilograms for mass or cubic meters for volume. These units change with the size of the system being measured. In contrast, intensive quantities are typically measured in intensive units, such as degrees Celsius for temperature or pascals for pressure. These units remain constant regardless of the size of the system.

Examples

Some common examples of extensive quantities include mass, volume, energy, and charge. These quantities increase or decrease with the size of the system. For instance, the total energy of a system is directly proportional to its size. Intensive quantities, on the other hand, include temperature, pressure, density, and concentration. These quantities remain constant regardless of the size of the system. For example, the temperature of a substance does not change with the amount of the substance present.

Relationship

Extensive and intensive quantities are related through the concept of density. Density is an intensive quantity that is derived from extensive quantities such as mass and volume. The density of a substance is defined as its mass per unit volume. While mass and volume are extensive quantities, density is an intensive quantity that remains constant regardless of the size of the system.

Measurement

When measuring extensive quantities, the total value of the quantity is calculated by summing the values for each component of the system. For example, to determine the total mass of a system, the masses of all the individual components are added together. In contrast, measuring intensive quantities involves determining the value of the quantity for a single component of the system. For instance, to measure the temperature of a substance, a thermometer is used to determine the temperature of a small sample of the substance.

Applications

The distinction between extensive and intensive quantities is important in various fields of science and engineering. In thermodynamics, for example, extensive quantities such as energy and entropy play a crucial role in determining the behavior of systems. Intensive quantities such as temperature and pressure are used to describe the state of a system without reference to its size. Understanding the difference between these two types of quantities is essential for accurate measurement and analysis in these fields.