Problem 3 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Among the following, the set of parameters that represents path functions. is:(A) \(q+w\) (B) \(q\) (C) \(w\)

Step-by-Step Solution

Answer

The path functions are (B) \(q\) and (C) \(w\).

Step 1: Understanding Path and State Functions

First, understand the concept of path and state functions. State functions depend only on the initial and final states of the system, not on how the change is made. Examples include internal energy (\(U\), enthalpy (\(H\), and entropy (\(S\). On the other hand, path functions depend on the path taken to reach one state from another, such as heat (\(q\) and work (\(w\).

Step 2: Analyze Provided Options

Look at the given options: (A) \(q+w\), (B) \(q\), and (C) \(w\). Here, \(q\) represents heat and \(w\) represents work. Both \(q\) and \(w\) are path functions, as their values depend on the process or path followed between two states.

Step 3: Evaluating Each Option

Evaluate each of the options to determine if they are path functions. \(q+w\), although it includes both \(q\) and \(w\), represents the change in internal energy (\(\Delta U\)), which is a state function as per the first law of thermodynamics: \(\Delta U = q + w\). This means \(q+w\) is not a path function. Subsequently, both \(q\) and \(w\) independently are path functions.

Step 4: Identify the Correct Set of Path Functions

Both option (B) \(q\) and option (C) \(w\) are path functions. Hence, these are the parameters that represent path functions in the given options.

Key Concepts

Path Functions

In thermodynamics, the concept of path functions is crucial for understanding how energy transitions occur in different processes. Unlike state functions, which are independent of the path taken, path functions are entirely dependent on it. This means the value of a path function can vary greatly depending on how a process is executed. For path functions like heat ( q ) and work ( w ), their values are contingent upon the exact pathway followed during a process transition.
This dependency on the path makes them unique:

• They cannot be described merely by looking at the initial and final states.
• Their computation typically requires a detailed understanding of the specific changes happening to a system.

Understanding path functions is important because it provides insight into the energy changes associated with processes that involve specific ways of energy transfers. For instance, the work done by or on a system depends on the mechanism of energy exchange between the surroundings and the system.

State Functions

State functions are fundamental in thermodynamics for describing systems comprehensively. These are properties or quantities whose values are determined entirely by the system's current state, regardless of how that state was reached. Examples of state functions include internal energy ( U ), enthalpy ( H ), and entropy ( S ).
State functions are vital for a number of reasons:

• They simplify the analysis of thermodynamic systems because their changes depend only on the initial and final states, not on the process.
• This consistency allows them to be represented graphically on state diagrams.

Given that state functions rely solely on the state's position, they allow us to focus on system properties without worrying about the specific history of the system or the path taken.

First Law of Thermodynamics

The first law of thermodynamics is a powerful principle recognizing the conservation of energy. It asserts that energy cannot be created nor destroyed, only transferred or transformed. The law is mathematically represented by the equation: \[ \Delta U = q + w \] where \( \Delta U \) is the change in internal energy, \( q \) is the heat added to the system, and \( w \) is the work done on the system.
This law is fundamental as it helps us understand the total energy changes within a system. Its consequences are noteworthy:

• It imposes a balance on energy exchanges between a system and its surroundings, ensuring all energy changes can be accounted for through heat and work.
• It underlines the link between a system's internal energy changes and the energy transferred via heat and work, emphasizing the broader implications of path and state functions in thermodynamics.

By grasping the first law, students can see clear connections between thermodynamic processes and energy flows in any physical or chemical change.