# Physics with Calculus/Thermodynamics/Intensive and Extensive Properties

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Thermodynamic properties can be divided into two categories. Properties that are proportional to the size of the sample are extensive properties. Examples of extensive properties are number of molecules N, or moles n, sample mass ms, volume V, internal energy U, and entropy S, among others. Extensive variables have definite values regardless of whether or not a sample is in a state of equilibrium.

Properties that are not proportional to the sample size are called intensive properties. Examples of intensive properties are pressure P, temperature T, density ρ, heat capacities Cv, Cp, and rms velocity vrms. When a sample is in a state of equilibrium the values of all intensive properties will be uniform throughout the sample. However, when a sample undergoes a rapid transition from one equilibrium state to another, the value of intensive parameters can vary wildly from location to location and from instant to instant.

A quasistatic transition from one state to another is carried out gradually with intensive properties not varying from location to location. As the transition proceeds the intensive properties will change from their initial to their final values but the incremental changes are simultaneous at all locations in the sample. One can say that at each step along a quasistatic process, the sample is in equilibrium with itself.

Transitions are driven when the intensive parameters of the sample are not equal to those of the surroundings. An object at a low temperature exposed to a reservoir at a high temperature attempts to come to equilibrium by absorbing heat. A high pressure gas expands a piston against atmospheric pressure. A quasistatic process that is driven by only infinitesimal differences between the intensive parameters of the sample and surroundings is called a reversible process.