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

Entropy, denoted as (S), is a fundamental concept in thermodynamics related to the disorder or randomness within a physical system. It's often described as a measure of the spread or dispersion of energy within a system and plays a key role in determining the direction of heat transfer and the efficiency of engines.
For instance, during any spontaneous process, the total entropy of a system and its surroundings always increases. This is encapsulated in the Second Law of Thermodynamics, which states that the total entropy of an isolated system can never decrease over time. Appreciating the role of entropy in chemical reactions helps us understand why certain reactions occur naturally while others do not.

Enthalpy, represented by (H), is a state function that refers to the total heat content of a system. It's often considered synonymous with the term 'heat' in constant pressure systems. However, enthalpy is a broader concept that encompasses the internal energy of the system plus the product of pressure and volume (PV).
The change in enthalpy ()(). However, since it also considers heat under constant pressure, this function is particularly useful for chemists and engineers working with thermochemical processes, like combustion or phase transitions.

Temperature, symbolized by (T), is a measure of the average kinetic energy of the particles in a system. In thermodynamics, temperature is a fundamental determinant of the direction of heat transfer: heat naturally flows from a warmer object to a cooler one until thermal equilibrium is reached.
Understanding how temperature affects entropy and enthalpy can provide insights into the complex behaviors of chemical and physical systems. For example, at higher temperatures, substances will have higher entropy because the increased kinetic energy of particles leads to greater disorder. The intricate interplay of temperature with other thermodynamic properties lies at the heart of energy transfer and transformation processes.

Heat, often represented by the symbol (q), is a form of energy transfer between systems or a system and its surroundings. It occurs due to a temperature difference and flows spontaneously from warm to cold regions. Unlike state functions such as entropy and enthalpy, heat is a path-dependent quantity.
The measurement of heat — called calorimetry — is vital for understanding reactions and processes, like how much energy is released during combustion or absorbed during melting. Heat plays a crucial role in phase transitions and chemical reactions, where it can be absorbed or released, known as endothermic and exothermic processes, respectively.

Work, indicated by (w), in the context of thermodynamics, refers to the energy transferred when a force acts upon an object to cause displacement. In thermodynamic processes, work can be done by or on the system, such as when a gas expands against a piston. Similar to heat, work is not a state function, as it also depends on the path taken, not just the initial and final states.
The concept of work is crucial in understanding energy conservation and conversion in physical systems, such as in heat engines where work is extracted from heat energy. It's the interplay of work and heat that underpins the operation of countless mechanical devices and industrial processes, demonstrating the fundamental nature of energy transformation in applied thermodynamics.