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 state function is a property of a thermodynamic system that depends only on its current state, such as temperature, pressure, and chemical composition, and not on the path used to reach that state. An example of a state function is Internal Energy (U), while an example of a non-state function is Heat (Q). Yes, the volume of a system is a state function, as it depends only on its current state and not on how the system achieved its volume or what path was taken.

Step-by-step solution

Understanding the term "State Function"

A state function is a property of a system in thermodynamics that depends only on its current state (temperature, pressure, and chemical composition), and not on the path used to reach that state. In other words, state functions are independent of their history or any specific process.

Examples of State Function and Non-State Function

1. Example of a state function: Internal Energy (U) - It is a property of a thermodynamic system that depends only on the current state of the system, not on how that state was achieved. It represents the stored energy within the system and can be related to the system's temperature and chemical composition. 2. Example of a non-state function: Heat (Q) - Heat is the energy transferred between a system and its surroundings due to a difference in temperature. It is not a state function because the heat transferred depends on the specific path taken during the process.

Volume as a State Function

Yes, the volume of a system is a state function. This is because the volume of a system only depends on its current state, such as pressure and temperature, and not on how the system achieved its volume or what path was taken. So, the system's volume is independent of its history or any specific process.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It concerns the laws governing the conversion of energy from one form to another and the rules that dictate the behavior of matter interacting with energy. In the context of thermodynamics, a state function is an important concept as it helps scientists understand the intrinsic properties of a system. This branch of science applies to various fields, including physics, chemistry, engineering, and even biology. Thermodynamics allows us to discover how energy conversions impact the system's state, whether it's in terms of temperature, pressure, or chemical makeup.

Internal Energy

Internal energy, often represented by the symbol \( U \), is a crucial concept in thermodynamics. It is a state function, meaning that it depends solely on the system's current state rather than the path by which the system arrived at that state. Internal energy encompasses all forms of energy contained within the system, such as kinetic and potential energy at the molecular level. It is intrinsic to the substance and is essential for understanding how energy is stored and transferred. For example, changes in internal energy can arise due to variations in temperature, phase changes, or chemical reactions within the system. Because it is a state function, measurements of internal energy changes are path-independent and provide a clear representation of the system's energy content at any given state.

Heat Transfer

Heat transfer is the movement of energy from one body or system to another due to a temperature difference. Unlike state functions, it is not independent of the path; rather, the amount of heat transferred depends significantly on how the transfer occurs. Three primary modes of heat transfer include conduction, convection, and radiation.

• **Conduction**: Direct transfer of heat through a material, requiring physical contact.
• **Convection**: The transfer of heat through fluid movement, which can be due to density differences or external forces.
• **Radiation**: Transfer of energy through electromagnetic waves, such as heat from the sun.

Understanding heat transfer is essential in thermodynamics since it helps us analyze how energy enters or leaves a system, influencing its state and properties.

Volume as State Function

Volume is indeed a state function. This means that the volume of a system depends only on the system's current conditions, such as pressure and temperature, and is not influenced by the pathway taken to reach those conditions. In thermodynamic processes, although volume can change, the end result or final volume solely depends on the final state rather than the process path. This characteristic makes the volume a reliable and constant property when analyzing systems in thermodynamics, as it shows the capacity of a system to contain matter under specific conditions. Since volume is unaffected by the history or transitions a system undergoes, it remains a vital example of a state function in the study of thermodynamic properties and changes.