Question

Can the value of an intensive property be uniform with position throughout a system? Be constant with time? Both?

Short answer

Yes, an intensive property can be uniform with position, constant with time, or both.

Step-by-step solution

Understand the Definition of Intensive Property

An intensive property is a physical property that does not depend on the system size or the amount of material in the system. Examples include temperature, pressure, and density.

Uniform with Position

An intensive property can be uniform with position throughout a system if it has the same value at every point in the system. For instance, in a well-mixed solution, the temperature can be the same throughout the entire volume.

Constant with Time

An intensive property can also be constant with time if it does not change as time progresses. For example, the pressure inside a sealed rigid container remains constant over time if no external factors influence it.

Both Uniform with Position and Constant with Time

It is possible for an intensive property to be both uniform with position and constant with time. For instance, the temperature in a well-insulated, well-mixed system can remain the same throughout the system and over time.

Key concepts

thermal equilibrium

Thermal equilibrium occurs when two or more subsystems have no net exchange of energy through heat. This means that the temperatures of the subsystems are equal. When this state is reached:

• Heat energy is uniformly distributed.
• No heat flows between different parts of the system.

In other words, thermal equilibrium ensures that the temperature is the same throughout all parts of the system. This fits our exercise where the temperature, an intensive property, can remain uniform with position. It also stays constant over time, as long as no external forces disturb the system. Think about when you prepare a cup of coffee and let it sit; after some time, it reaches thermal equilibrium with the room.

properties of matter

Properties of matter tell us how substances behave and interact under different conditions. These are divided into intensive and extensive properties. Intensive properties do not change with the amount of substance or its size, making them very useful in identifying and describing materials. Examples include:

• Density
• Boiling point
• Pressure
• Temperature

In our exercise, we focus on how intensive properties can be uniform with position and constant with time. Across a uniform medium, intensive properties need to be the same at every location to maintain a steady state. For instance, the density of water in a sealed container remains the same everywhere inside, ensuring equilibrium if undisturbed.

steady-state conditions

Steady-state conditions imply that various properties within a system do not change over time. When a system is in a steady state:

• Properties such as temperature, pressure, and density are constant.
• No gradients (differences) in these properties exist within the system.

For example, consider a well-insulated room maintained at a constant temperature by an air conditioner. The air inside the room reaches a steady state when the temperature becomes uniform and stable over time. This ties back to our exercise in which an intensive property like temperature can stay both uniform in position and constant over time, perfectly illustrating a steady state. This concept helps us understand environments where conditions do not fluctuate, making them predictable and stable for analysis.