Question

Which of the following are not state functions: \(S, H, q, w, T ?\)

Short answer

Heat (q) and work (w) are not state functions.

Step-by-step solution

Understanding State Functions

A state function is a property whose value does not depend on the path taken to reach that specific value. In other words, a state function depends only on the initial and final states of a system, not on how the system arrived at that state.

List of Properties

The properties given in the exercise include entropy ( S ), enthalpy ( H ), heat ( q ), work ( w ), and temperature ( T ). We need to determine which of these are state functions.

Analyzing Entropy (S) and Enthalpy (H)

Both entropy ( S ) and enthalpy ( H ) are state functions because they depend only on the state of the system, not how it was achieved. For any given state of a system, S and H are defined regardless of the processes that led to those states.

Analyzing Heat (q) and Work (w)

Heat ( q ) and work ( w ) are not state functions. They are path functions because their values depend on the specific path taken by a system to change states. The amount of heat transferred or work done can vary based on how the change is carried out.

Analyzing Temperature (T)

Temperature ( T ) is a state function. Like entropy and enthalpy, the temperature of a system is determined only by its current state, not on the process used to reach that temperature.

Conclusion

Based on the analysis, the properties that are not state functions among the given options are heat ( q ) and work ( w ).

Key concepts

Path Functions

In thermodynamics, path functions are properties that depend on the specific path taken to reach a particular state. Unlike state functions, they are not determined solely by the initial and final states. Instead, the quantity of a path function can vary depending on how a change is realized.

Key examples of path functions:

• Heat (q): The amount of heat transferred depends on the way energy is exchanged between a system and its surroundings. Different paths can lead to different heat values.
• Work (w): Just like heat, the work done by or on a system is path-dependent. For instance, compressing a gas slowly versus quickly can result in different quantities of work.

Understanding path functions is crucial because it helps in analyzing energy exchanges in engineering and natural processes. These concepts are vital in many real-world applications.

Entropy

Entropy, denoted as \( S \), is a key concept in thermodynamics. It measures the disorder or randomness of a system. Importantly, entropy is a state function, which means it depends only on the current state of the system, not the path taken to reach it.

Why entropy matters:

• Entropy helps explain the direction of spontaneous processes. In isolated systems, processes tend to increase the total entropy.
• It is closely related to the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time.

Entropy is also used to determine the efficiency of thermodynamic cycles, playing a crucial role in engines, refrigerators, and many other technologies.

Enthalpy

Enthalpy, represented by \( H \), is a measure of the total heat content in a system. It is particularly useful in processes occurring at constant pressure, such as chemical reactions. Like entropy, enthalpy is a state function, meaning it is determined by the state of the system.

Key points about enthalpy:

• In chemical reactions, the change in enthalpy \( \Delta H \) can help determine if a reaction is endothermic (absorbing heat) or exothermic (releasing heat).
• It allows us to understand and calculate the heat exchange with the surroundings, useful in designing energy-efficient systems.
• Enthalpy simplifies the analysis of processes, particularly when dealing with pressure-volume work.

In essence, enthalpy helps predict energy changes and is an integral part of both academic studies and practical applications.

Temperature

Temperature, denoted \( T \), is a fundamental concept in thermodynamics. It is a measure of the average kinetic energy of particles in a system and is essential for understanding heat and thermal energy. Temperature is a state function, meaning it relies solely on the present state of the system.

Significance of temperature:

• Temperature provides a quantifiable measure for thermal energy which is pivotal in understanding heat transfer and thermodynamic processes.
• It establishes thermal equilibrium between systems. Two systems in thermal contact are in equilibrium when they are at the same temperature.
• Temperature scales like Celsius, Fahrenheit, and Kelvin are used universally, which help in standardizing measurements in scientific experiments and everyday life.

Comprehending temperature is vital for explaining how heat transfer occurs and how it impacts the behavior of different materials and processes.