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 \(\mathrm{B}\) by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy? [2003] (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; the correct answer is (d).

Step 1: Understanding Internal Energy Change

The internal energy change for the process from state A to state B is given as 40 kJ/mol. This information tells us the energy required or released as the system transitions from state A to B.

Step 2: Concept of State Function

Internal energy is a state function, meaning its change depends only on the initial and final states, not the path taken. Thus, the internal energy change from A to B and then back to A must sum to zero because the system returns to the initial state.

Step 3: Calculating Net Change

As internal energy is a state function, the net change in internal energy after returning to the initial state (A to B to A) is zero. This is because the system ends where it started, regardless of the path taken (reversible or irreversible).

Step 4: Conclusion

Given that the system starts and ends at the same state, the net change in internal energy is zero. This is independent of whether the path between those states is reversible or irreversible.

Key Concepts

Internal Energy

Internal energy is a fundamental concept in thermodynamics. It represents the total energy contained within a system, comprising both its kinetic and potential energies. Internal energy changes as a system undergoes different processes, such as heating, cooling, or performing work.
For example, if a gas is heated, its internal energy increases due to the higher kinetic energy of its molecules. Similarly, if a gas expands and performs work, some of its internal energy is transferred to the surroundings.
In the exercise, the change in internal energy from state A to state B is given as 40 kJ/mol. This indicates how much energy is absorbed or released as the system transitions between these two states.

State Function

A state function is a property of a system that depends solely on the system's current state, not on the path taken to achieve that state. Examples of state functions include pressure, volume, temperature, and internal energy.
The key characteristic of a state function is its path independence. This means that when calculating changes in state functions, we only consider the difference between the initial and final states.

• The internal energy of a system, for instance, remains consistent regardless of the process path.
• Therefore, the internal energy change for any round trip, where the system returns to its original state, will be zero.

Understanding that internal energy is a state function helps in determining that the net change in internal energy for the given exercise is zero.

Reversible Path

A reversible path in thermodynamics refers to a process that occurs so slowly that the system remains in equilibrium throughout the process. It is an idealized concept because real processes aren't perfectly reversible, but it helps in understanding thermodynamic principles.
In a reversible process:

• Changes occur infinitesimally slowly.
• The system and surroundings can return to their original states with no net changes.

In the exercise, when the system goes from state A to B via a reversible path, it's as if the system has the maximum efficiency in energy usage, avoiding energy dissipations associated with fast or uncontrolled paths.

Irreversible Path

An irreversible path, conversely, involves processes that happen quickly or result in non-equilibrium states. These include heat exchange with a large temperature difference or rapid expansion of gases.
Characteristics of irreversible processes include:

• The process is spontaneous or rapid.
• There is energy dissipation due to factors like friction, turbulence, or non-uniform temperature.

In the context of the exercise, returning from state B to A along an irreversible path means that, although energy might be lost to the surroundings, the starting and ending states are the same. Therefore, as internal energy is a state function, the net change remains zero.