Problem 13 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

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

Step 1: Understand the concept of state functions

State functions are properties that depend only on the current state of a system, not on the path taken to reach that state. Examples include temperature, pressure, volume, and enthalpy. Since they do not depend on the process, they remain unchanged if the state is the same.

Step 2: Analyze each statement

- Statement (a): Temperature is a state function because it indicates the thermal condition of a system at a particular state. - Statement (b): Work is NOT a state function, because it depends on the process used to move between two states. Work is path-dependent. - Statement (c): Change in state depends only on the initial and final states and not on the path taken, which is true for state functions. - Statement (d): Work appearing at the boundary of a system is a characteristic behavior of work, as it involves energy transfer across a boundary.

Step 3: Identify the false statement

Since work is path-dependent and not solely determined by the initial and final states, statement (b) is false. Unlike work, a genuine state function does not rely on the path taken.

Key Concepts

State Functions and Their Unique Characteristics

In thermodynamics, a state function is a property that depends solely on the current state of the system, irrespective of how that state was achieved. Key examples of state functions include:

• Temperature
• Pressure
• Volume
• Enthalpy

State functions are intrinsic properties, much like a snapshot that captures the current conditions of a system. They remain unchanged as long as the system is in that particular state. This means that the value of a state function is the same no matter the path taken to achieve that particular state. For instance, whether water is heated slowly or quickly to a certain temperature, its temperature will be the same at that final state. This unique characteristic of state functions makes them quite valuable in thermodynamics, as they provide crucial information about the system at any given point.

Path-Dependent Processes Explained

Unlike state functions, path-dependent processes are those where the final value depends on the specific route taken to reach the end state. Common path-dependent quantities in thermodynamics include:

• Work
• Heat

The concept of path-dependent processes can be likened to a journey where the path taken matters. Imagine taking different routes to climb a mountain; the energy expended will vary depending on whether you take a steep path or a gentler one. This reflects how work and heat depend on the specific process. Because these quantities do not solely depend on initial and final states, we cannot describe them as state functions. This distinction is crucial in thermodynamics, as it influences how these variables behave during various processes and transformations.

Understanding System Boundaries in Thermodynamics

In thermodynamics, the concept of a system boundary is very important. System boundaries define the limits of the system being studied and how it interacts with its surroundings. There are several types of boundaries, including:

• Fixed boundary
• Movable boundary
• Rigid boundary
• Flexible boundary

These boundaries determine whether and how energy and matter can cross the border of a system. For example, a "diathermic" boundary allows heat to pass through, whereas an "adiabatic" boundary does not permit any heat transfer. Understanding boundaries helps to define the system's interactions with its environment, such as the work done when the system expands against an external pressure. By clearly recognizing the type of system boundary, one can better assess the thermodynamic processes taking place, particularly in evaluating path-dependent processes like work, which is centered around energy crossing the boundary.