Question

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of a system a state function? Why or why not?

Short answer

(a) A state function is a property of a system that depends only on its current state, which is determined by factors such as temperature, pressure, and composition, and not on the path taken to achieve that state. (b) An example of a state function is internal energy (U), while heat (q) and work (w) are examples of non-state functions. (c) Yes, the volume of a system (V) is a state function because it only depends on the current state of the system and not on the history or process taken to reach that state.

Step-by-step solution

Definition of State Function

A state function is a property of a system that depends only on its current state, which is determined by factors such as temperature, pressure, and composition, and not on the path taken to achieve that state. In other words, state functions are independent of the process or the history of the system.

Example of a State Function and a Non-State Function

An example of a state function is the internal energy of a system (U). It is a state function because it only depends on the current state of the system and not how we reached that state. Suppose we change the temperature of a gas, the final internal energy of the gas is the same regardless of whether we heated it quickly or slowly, in steps or continuously. On the other hand, heat (q) and work (w) are examples of non-state functions or process functions. They depend on the specific process or pathway taken to reach a particular state. Suppose we have a system going from an initial state to a final state; the heat and work would be different if the process was done isothermally (i.e., at constant temperature) or adiabatically (i.e., no heat exchange).

Volume as a State Function

The volume of a system (V) is a state function because it only depends on the current state of the system and not on the history or process taken to reach that state. For example, if a gas is compressed to half its initial volume, the final volume is the same, regardless of whether the compression was done slowly or quickly, or even in a multistep process. The volume only depends on the current pressure, temperature, and composition of the system and is, therefore, a state function.

Key concepts

Thermodynamics

Thermodynamics is a fascinating branch of physics that explores how energy is transferred and transformed in systems. At its core, thermodynamics deals with the principles governing the movement of heat and how it converts into work.
It helps us understand how energy changes occur in everything from engines to biological processes.
Within the framework of thermodynamics, different properties are defined to describe the state of physical systems. These include temperature, pressure, and volume.
Understanding these properties can allow prediction and analysis of the system's behavior.
To fully grasp thermodynamics, we also explore the concept of equilibrium. In a system at equilibrium, the state remains constant over time, unless disturbed by an external force. All variables describing the system's state remain stable, making predictions about the system simpler and manageable.
Applications of thermodynamics range widely in all fields of science including chemistry, engineering, and environmental science. The laws of thermodynamics are powerful tools for solving real-world problems and optimizing processes.

Internal Energy

Internal energy is a key concept in thermodynamics and refers to the total energy contained within a system.
It includes all forms of kinetic and potential energy at the molecular level but excludes energy due to motion or energy stored in the external environment.
Internal energy ( U ) is considered a state function, meaning it relies solely on the current state of the system, such as its temperature and pressure.
It does not depend on the path taken to reach that state.
For instance, whether a gas is heated rapidly or slowly doesn't alter the final internal energy, if the initial and final states are the same.
There are two primary ways to change a system's internal energy:

• Heat Transfer: When heat is added, the internal energy of the system tends to increase.
• Work Done: Performing work on a system, like compressing a gas, can also change internal energy.

This concept is vitally useful in calculating energy changes in physical and chemical processes.

Process Functions

Process functions are different from state functions, as they depend on the path taken to transition between two states.
These include heat (q) and work (w), and they describe energy transfer across the system boundary.
Heat is the energy transferred due to a temperature difference between the system and its surroundings.
Work, on the other hand, represents energy exchanged due to motion against an opposing force.
Unlike state functions, process functions can vary significantly depending on the method employed to transition from one state to another.
For example, the amount of heat and work can vary if a gas is heated at constant temperature (isothermal process) versus when no heat is exchanged (adiabatic process).
Understanding their dependency on the path is crucial for processes design and analysis. While individual values for heat and work may vary, their total can determine the change in internal energy, as stated by the first law of thermodynamics: \[\Delta U = q + w\]This relationship reveals the connection between state and process functions in a comprehensive framework.