Distinguish between state function and path functions with examples. A cyclic process may be defined as the one in which after a series of changes, the system is brought back to its initial conditions. What would be the change in a state function in a cyclic process?
The correct answer and explanation is :
State Functions vs. Path Functions
State functions and path functions are two key concepts in thermodynamics that describe different properties of a system.
- State Functions: A state function is a property whose value depends only on the state of the system, not on the path taken to reach that state. In other words, the value of a state function is determined by the system’s current condition (e.g., temperature, pressure, volume) and not by how the system got there. The change in a state function is independent of the process, as long as the initial and final states are the same. Examples of state functions:
- Internal energy (U): The total energy contained in a system.
- Enthalpy (H): The heat content of a system, at constant pressure.
- Pressure (P): The force exerted per unit area by a system on its surroundings.
- Temperature (T): A measure of the average kinetic energy of particles in the system.
- Entropy (S): A measure of the disorder or randomness in a system.
- Path Functions: A path function is a property whose value depends on the path taken to reach a particular state. These are not determined solely by the state of the system but are influenced by the process or the series of steps the system undergoes. The work done and heat exchanged are typical examples of path functions. The amount of heat added or work done depends on the specific process, not just the initial and final states. Examples of path functions:
- Work (W): The energy transferred when a force is applied over a distance.
- Heat (Q): The transfer of thermal energy between systems.
Change in State Function in a Cyclic Process
In a cyclic process, the system undergoes a series of changes and ultimately returns to its initial state. Since the process returns to its original condition, the values of state functions (such as temperature, pressure, and internal energy) at the beginning and end of the cycle are identical.
Therefore, the change in a state function during a cyclic process is always zero. This is because state functions depend only on the initial and final states, and in a cyclic process, these states are the same. For example, if a system undergoes a cyclic process where it starts and ends at the same temperature and pressure, its internal energy and enthalpy will not change.
In contrast, the work done and heat exchanged, being path functions, can be non-zero even though the system returns to its initial state.
Thus, the key takeaway is that state functions are independent of the path and have zero net change in a cyclic process, while path functions can vary depending on the specific process taken.