Which of the following are state functions, and which are not? (a) The temperature of an ice cube (b) The volume of an aerosol can (c) The amount of time required for Paula Radcliffe to run her world-record marathon: 2:15:25

Verified step by step guidance

1. Understand the concept of a state function: A state function is a property whose value does not depend on the path taken to reach that specific value. It depends only on the current state of the system.
2. Identify if temperature is a state function: Temperature is a state function because it is a property that depends only on the current state of the system, not on how the system reached that state.
3. Identify if volume is a state function: Volume is a state function because it is a property that depends only on the current state of the system, not on the path taken to reach that state.
4. Consider if time is a state function: Time is not a state function because it depends on the path taken. The amount of time required for an event, like running a marathon, depends on the specific path or process taken.
5. Summarize: Temperature and volume are state functions, while time is not a state function.

Key Concepts

State Functions

State functions are properties of a system that depend only on its current state, not on the path taken to reach that state. Examples include temperature, pressure, volume, and internal energy. These properties are crucial in thermodynamics as they help describe the system's equilibrium state without considering the history of the system.

Path Functions

Path functions are properties that depend on the specific path taken to change the state of a system. Unlike state functions, they are not determined solely by the current state. Examples include work and heat, which vary based on the process used to transfer energy or change the system's state.

Examples of State vs. Path Functions

In the context of the question, temperature and volume are state functions because they describe the system's current state without regard to how that state was achieved. Conversely, the time taken to complete a marathon is a path function, as it depends on the specific conditions and pace of the run, making it not a state function.