Electrical conductivity is classified as an intensive property, meaning its value does not change regardless of the size or amount of the material being examined. This classification might seem counterintuitive, especially when considering how factors like wire length affect electrical performance. However, the conductivity of a specific material, such as copper, remains the same whether you are looking at a tiny sample or a massive block, provided environmental conditions like temperature are kept constant.
Distinguishing Intensive and Extensive Properties
Physical properties are categorized into two groups based on their relationship to the quantity of matter present in a sample. An intensive property is one that is independent of the amount of substance. For instance, the temperature of a glass of water is the same as the temperature of the water in a pitcher from which it was poured. Other examples of intensive properties include density and the boiling point of a substance.
Extensive properties, conversely, are those whose values are directly proportional to the amount of substance in the system. The most straightforward examples are mass and volume; doubling the amount of a substance will double both its mass and its volume. Length and total energy are also considered extensive properties because they are additive when two subsystems are combined.
Why Electrical Conductivity Is Intensive
Electrical conductivity (\(sigma\)) is an intrinsic characteristic of a material, reflecting its inherent ability to allow electric charge to flow through it. This property is determined primarily by the material’s atomic structure, specifically the availability of free-moving electrons or ions. The value of conductivity for a substance is characteristic of that material under specific conditions, such as temperature and pressure.
If a copper wire is cut into two pieces, the conductivity of each resulting piece remains the same as the original wire because the underlying material is unchanged. Conductivity is conceptually measured as the ease with which current flows through a standardized unit volume of the material. This independence from sample size or geometry is the reason electrical conductivity is classified as an intensive property.
The Relationship Between Conductivity, Resistance, and Sample Size
The concept of resistance often causes confusion when trying to classify conductivity, because resistance changes with the size of an object. Electrical resistance (\(R\)) is an extensive property, meaning it depends directly on the physical dimensions of the conductor. The resistance of a wire increases if its length (\(L\)) is increased, and the resistance decreases if its cross-sectional area (\(A\)) is made larger.
This relationship is mathematically expressed by the formula \(R = rho (L/A)\). Here, \(R\) is the resistance, \(L\) is the length, and \(A\) is the area. The term \(rho\) (rho) in this equation is the electrical resistivity, which is itself an intensive property.
Resistivity is defined as the inverse of conductivity (\(rho = 1/sigma\)), and it represents the material’s inherent opposition to electrical flow. The formula demonstrates how the extensive property, resistance (\(R\)), is calculated using the material’s intensive property, resistivity (\(rho\)), and its extensive dimensions (\(L\) and \(A\)). While a long, thin copper wire has a higher resistance than a short, thick copper wire, both wires possess the same resistivity and conductivity. This difference highlights that conductivity and resistivity are characteristic of the material itself, while resistance is a function of both the material and its specific shape.