Question

Which of the following statements is false? (a) Work is a state function. (b) Temperature is a state function. (c) Change of state is completely denned when initial and final states are specified. (d) Work appears at the boundary of the solution.

Short answer

Statement (a) is false; work is not a state function.

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. Examples include temperature, pressure, and internal energy. These properties are determined only by the current state of the system, not how it got there.

Analyzing Statement (a)

Statement (a) claims that work is a state function. Work is dependent on the path taken between two states and not solely on the initial and final states. Therefore, work is not a state function.

Analyzing Statement (b)

Statement (b) claims that temperature is a state function. Temperature is indeed a state function since it only depends on the state of the system, irrespective of how the system arrived at that state.

Analyzing Statement (c)

Statement (c) asserts that a change of state is fully defined when initial and final states are specified. This is true for state functions, as they only require initial and final states for determination, without regard to the path taken.

Analyzing Statement (d)

Statement (d) states that work appears at the boundary of the system. Work is an energy transfer across the boundaries of a system, and thus this statement is true.

Determining the False Statement

Upon analyzing each statement, statement (a) is the false one since work is not a state function, unlike what's claimed.

Key concepts

Work as a Path Function

In thermodynamics, work is known as a path function. This means that the amount of work done by a system depends on the specific path taken to transition between two states, rather than just the initial and final states themselves. Imagine standing at the base of a hill with multiple pathways to the top. Some paths may be steep and direct, while others might wind gently. The energy or effort (work) required will vary based on the route chosen. Similarly, in physics, work is affected by factors such as distance and force direction along the path. Due to this dependency on the transition path, work is not considered a state function, distinguishing it from other thermodynamic properties like temperature and pressure.

State Properties

State properties, also known as state functions, are unique because their values are determined only by the current state of the system, not the path used to arrive there. Examples of state functions include:

• Temperature: Reflects the thermal condition of the system.
• Pressure: Describes the force exerted per unit area within the system.
• Internal Energy: The total energy contained within a system.

These properties remain constant for a given state regardless of the series of processes that led to that state. In practice, knowing just the initial and final states is enough to determine the change in any state property, simplifying calculations and analyses. Because these values are consistent for a state, state properties are essential for comprehensive and accurate thermodynamic analysis. They provide reliable benchmarks for evaluating energy changes.

Thermodynamic Analysis

Thermodynamic analysis involves assessing systems based on how energy, in forms such as heat and work, transits across boundaries. This type of analysis helps us understand processes like power generation, combustion, and refrigeration. One crucial element in this examination is identifying which properties are state functions versus path functions, as this distinction influences how calculations are performed. For instance, since work is a path function, it's essential to specify the particular process path in questions involving work calculations. However, for properties like internal energy, which is a state function, only the initial and final states are necessary to find change amounts. Such understanding aids engineers and scientists in optimizing processes by accurately predicting how modifications will impact energy transfer and system efficiency.