Question

Which one of the following statements is false? (a) Temperature is a state function (b) Work is a state function (c) Change in the state depends upon initial and final state (d) Work appears at the boundary of the system

Short answer

Statement (b) 'Work is a state function' is false.

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. Temperature is a state function, as it depends only on the state of the system.

Analyzing 'Work' as a State Function

Work is not a state function because the amount of work done depends on the path taken during a process. Different paths between two states can involve different amounts of work.

Evaluating Change in State Dependency

The change in the state of a system depends only on the initial and final states, not on how the transition between these states occurs. This is consistent with the concept of state functions.

Boundary Work Characteristics

Work is an energy transfer that appears at the boundary of the system and depends on the path, which fits its definition. This statement is true.

Identifying the False Statement

Based on the analysis, the statement that 'Work is a state function' is false because work depends on the path, not just the initial and final states.

Key concepts

Temperature as a State Function

In thermodynamics, state functions are properties dependent solely on the state of the system, not the path taken to reach that state. Temperature exemplifies this beautifully. Regardless of how a system achieves a particular temperature, it is the same once the final state is reached. This implies that measurements and calculations involving temperature can remain consistent as long as the system's state is unaltered. For instance, if you heat a pot of water to 100 °C, the temperature is simply 100 °C, whether you heat it quickly or slowly. Thus, knowing the temperature provides valuable insight into the system's state without needing to recount its history or the path it took to get there.

Work and Path Dependence

Unlike temperature, work is not a state function because it heavily depends on the route taken during a process. This means the amount of work done can vary widely based on the pathway. In a thermodynamic process, work can involve different variables such as pressure or volume changes. For example, compressing a gas quickly or slowly can yield different amounts of work, showcasing its path-dependent nature. So, while two systems may start and end at identical states, the journey between these points can yield different work values. Understanding this concept is crucial, especially in engineering and physics, where efficiency and energy transformations are key.

State Change Dependence

When considering the change in a system's state, it is essential to understand that the start and finish are all that matter. The actual process or path taken doesn't influence this change if we are discussing state functions. This principle is fundamental in thermodynamics and is often used to simplify complex systems. The focus is on the initial and final states rather than every step in between. This allows for comparisons between different processes, as only the end conditions dictate the total change.

Energy Transfer in Thermodynamics

Energy transfer in thermodynamics, specifically through work and heat, is a cornerstone of understanding how systems interact with their surroundings.

• Work: Refers to energy transferred across the system's boundaries, dependent on the path taken by the system during a process.
• Heat: Another form of energy transfer, but unlike work, it is often associated with the transfer due to temperature differences.

These transfers are critical in driving operations in engines, refrigerators, and numerous other systems. Energy isn't created or destroyed—it simply changes form or moves across boundaries, embodying the first law of thermodynamics. Recognizing these transfers' roles helps in designing and analyzing systems to manage energy efficiently.