Problem 154 - A Complete Resource Book in Chemistry for JEE Main

Question

The internal energy change when a system goes from state \(\mathrm{A}\) to \(\mathrm{B}\) is \(40 \mathrm{~kJ} / \mathrm{mol}\). If the system goes from \(\mathrm{A}\) to B by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy? (a) \(40 \mathrm{~kJ}\) (b) \(>40 \mathrm{~kJ}\) (c) \(<40 \mathrm{~kJ}\) (d) zero

Step-by-Step Solution

Answer

The net change in internal energy is zero, option (d) zero.

Step 1: Understanding Internal Energy

The internal energy of a system is a state function. This means that any change in internal energy depends only on the initial and final states of the system, and not on the path taken.

Step 2: Analyzing the Given Path

The system goes from state A to state B by a reversible path. When the system returns to state A from B by any path, including an irreversible one, since internal energy is a state function, the net change in internal energy over this complete cycle should be considered.

Step 3: Calculating Net Change in Internal Energy

Since internal energy is a state function, the net change in internal energy for the process where the system goes from A to B and back to A is zero. This is because the initial and final states are the same.

Step 4: Evaluating the Options

Given the net change in internal energy is zero for the complete cycle of going A to B and back to A, the correct answer is option (d) zero.

Key Concepts

State Function

Internal energy is a key concept in thermodynamics, especially when discussing state functions.
A state function is a property of a system that depends only on the current state of the system, and not on how it arrived there.
This means that regardless of the process or path taken to get from one state to another, the change in a state function is always determined by the difference between the final and initial states.

• Path Independence: Unlike path functions such as work and heat, state functions are path-independent.
• Example of State Functions: Internal energy, enthalpy, and entropy are common examples of state functions.

Understanding that internal energy is a state function helps simplify calculations in thermodynamics, because you can focus on the initial and final states rather than the details of the process that connects them.

Reversible Path

A reversible path in thermodynamics refers to a process carried out in such a way that the system and its surroundings can be returned to their original states without any net change.
This is an idealization because, in the real world, all processes have some degree of irreversibility.

• Quasi-Static Process: A reversible path can be seen as a series of quasi-static processes, where the system is always an infinitesimal step away from equilibrium.
• Efficiency: Reversible processes are maximally efficient because they do not generate excess entropy.

In the context of internal energy, a reversible path from state A to state B would involve precisely calculated changes that maintain equilibrium throughout the process.

Irreversible Path

Unlike a reversible path, an irreversible path is one where the process generates entropy, and often involves a spontaneous change.
This type of path cannot be undone without leaving a trace on the system and its surroundings.

• Entropy Increase: Irreversible processes are accompanied by an increase in the total entropy of the system and its surroundings.
• Real-World Example: Most natural processes, such as the expansion of a gas into a vacuum, are irreversible.

When a system follows an irreversible path, energy disperses, making it impossible to return to the original state without external intervention.

Thermodynamic Cycle

A thermodynamic cycle refers to a series of processes that return a system to its initial state at the end of the cycle.
During a complete cycle, even though work and heat may be exchanged, state functions like internal energy must return to their original values.

• Cyclic Process: In a cycle, the system undergoes various stages but returns to its starting point, resulting in a net change of zero for state functions.
• Zero Net Change in Internal Energy: Since internal energy is a state function, in a thermodynamic cycle from A to B and back to A, the net change in internal energy is zero.

This fundamental understanding of cycles allows for the analysis of engines and refrigerators, which rely on repeating cycles to perform work or transfer heat.