Question

Indicate whether each statement is true or false. (a) \(\Delta S\) depends on whether the process is reversible or irreversible. \((\mathbf{b})\) If a system undergoes an irreversible change, the entropy of the universe increases. (c) Only if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings, the system undergoes a reversible process. (d) If the entropy change of the system is zero, the system undergoes a reversible process.

Short answer

(a) False - \(\Delta S\) is a state function and does not depend on whether the process is reversible or irreversible. (b) True - If a system undergoes an irreversible change, the entropy of the universe will increase. (c) True - A system undergoes a reversible process if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) False - A zero entropy change of the system does not necessarily imply a reversible process.

Step-by-step solution

Statement a: Is \(\Delta S\) dependant on whether the process is reversible or irreversible?

No, the change in entropy \(\Delta S\) is a state function, meaning it depends only on the initial and final states of the system and not on the path taken between those states. Thus, it doesn't matter if the process is reversible or irreversible. This statement is False.

Statement b: If a system undergoes an irreversible change, does the entropy of the universe increase?

Yes, according to the second law of thermodynamics, if a process is irreversible, the total entropy of the universe must increase. This statement is True.

Statement c: Is a system undergoing a reversible process only if the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings?

Yes, for a reversible process to occur, the entropy change in the system must be equal and opposite to the entropy change in the surroundings, so the total entropy change in the universe is zero. This statement is True.

Statement d: If the entropy change of the system is zero, does the system undergo a reversible process?

No, a system having an entropy change of zero does not necessarily guarantee that it has undergone a reversible process. In some cases, the entropy of a system may not change during an irreversible process, such as an adiabatic free expansion of a gas. In this case, the entropy change of the system is zero, but the process is still irreversible. This statement is False.

Key concepts

Reversible Process

A reversible process is an idealized concept in thermodynamics. In these processes, changes occur so slowly that the system is always in equilibrium. This means that if you could reverse the process, the system and surroundings would return to their original states without any change in the overall entropy of the universe.
In reality, perfectly reversible processes do not occur, but understanding them is crucial for studying real-world systems. The main characteristics of a reversible process include:

• Equilibrium: The system remains infinitesimally close to an equilibrium state throughout the process.
• No Entropy Production: The total entropy change of the universe is zero, meaning any gain in entropy by the system is offset by an equal loss by the surroundings.
• Infinite Slowness: It requires infinitely slow operations, allowing for complete control over energy exchanges.

While this concept is theoretical, it serves as a benchmark for comparing real-world processes.

Irreversible Process

An irreversible process is a more realistic depiction of natural processes. These processes occur spontaneously and cannot be reversed without leaving changes in both the system and the surroundings. Unlike reversible processes, irreversible processes are associated with an increase in the total entropy of the universe.
The hallmark features of irreversible processes include:

• Spontaneous Nature: They occur naturally and can proceed without external intervention once started.
• Entropy Increase: According to the second law of thermodynamics, the entropy of the universe increases during an irreversible process. This is a key factor that distinguishes them from reversible processes.
• Finite Time and Energy Dissipation: These processes occur within a finite amount of time and often involve energy dissipation due to factors like friction and turbulence.

Understanding these processes helps in acknowledging the inherent inefficiencies present in real-world systems.

Second Law of Thermodynamics

The second law of thermodynamics is a fundamental principle governing the direction of spontaneous processes. It states that, in an isolated system, natural processes tend to move toward a state of maximum disorder or entropy. This law highlights the concept that the entropy of an isolated system will never decrease over time.
Key points to understand about the second law include:

• Entropy Increase: In any natural process, the total entropy of an isolated system always tends toward increase, not decrease.
• Direction of Processes: It provides a criterion for determining the direction of thermodynamic processes; processes naturally evolve towards states that increase the overall disorder.
• Efficiency Limit: The law imposes constraints on the efficiencies of heat engines, ensuring that they cannot completely convert heat to work without some loss as waste heat.

This law forms the basis for understanding why energy transfers are never 100% efficient and why perpetual motion machines are impossible.