Problem 4 - 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

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

Step 1: Understanding Path Functions

Path functions depend on the specific path taken by a system between two states. In thermodynamics, common path functions are heat ( q ) and work ( w ), as they vary depending on how a process is carried out.

Step 2: Identifying Path Functions

We need to identify which of the given options represent path functions. From the options given: (A) q + w . (B) q . (C) w . Both q (heat) and w (work) are path functions since they depend on the process.

Step 3: Evaluating Each Option

(A) q+w : The sum of heat and work is not a path function because it represents a state function (change in internal energy, ΔU , which is independent of the process path). (B) q : Heat is a path function, as it depends on the path and the method of transfer. (C) w : Work is a path function because it is dependent on the manner the system changes.

Step 4: Conclusion

The set of parameters that represent path functions from the options provided are options (B) q and (C) w , since both depend on how the process is executed.

Key Concepts

Path Functions

Path functions are a fundamental concept in thermodynamics that describe properties dependent on the path taken between two states. A key point about path functions is that their values are not solely determined by the initial and final states of a system; rather, they depend on the specific process or path taken during the transformation.

In simple terms, path functions can be thought of as journey-related properties. Just like the distance you travel can vary with the route chosen, path functions like heat and work vary depending on the way a process is carried out in a thermodynamic system. It's important to differentiate path functions from state functions, which are only concerned with the starting and ending points and not the path or process followed.

Understanding this distinction helps predict and control how processes occur within thermodynamic systems. Knowing that path functions depend on specific conditions allows engineers and scientists to manipulate systems for desired outcomes.

Heat (q)

Heat is one of the most common path functions in thermodynamics, indicated by the symbol \(q\). When heat is transferred between systems or a system and its surroundings, the path it takes is crucial to the amount of heat exchanged.

Key characteristics of heat as a path function include:

• Dependence on how energy is transferred: The amount of heat involved changes if, for example, energy is supplied quickly versus slowly.
• Varies with conditions: Specific details like the temperature difference between surroundings and the system impact how much heat is exchanged.

It is essential to remember that heat cannot be stored or possessed by a system intrinsically. Instead, it represents energy in transit due to temperature differences, distinctly linking it to the pathways and means of transfer utilized in a process.

Work (w)

Work, signified by \(w\), is another core path function in thermodynamics, directly tied to how a system interacts with its surroundings.

Understanding work as a path function involves recognizing several aspects:

• Dependence on process details: The work done by or on a system varies based on how forces are applied, making every scenario unique.
• Varies with the method of interaction: Whether a gas is compressed slowly or quickly will alter the amount of work done.

In simple terms, think of work as the outcome of energy transfer facilitated through mechanical means. It's all about the details: the path taken impacts how much work is done - quite like how traveling around hills or flat terrain changes the effort required to reach a destination.

The dynamic nature of work as a path function makes it critical for understanding energy exchanges during physical processes, whether expanding a gas or moving a piston in an engine.