Problem 18 - Chemistry: The Central Science

Question

Indicate whether each statement is true or false. (a) All spontaneous processes are irreversible. (b) The entropy of the universe increases for spontaneous processes. (c) The change in entropy of the surroundings is equal in magnitude and opposite in sign for the change in entropy of the system, for an irreversible process. (d) The maximum amount of work can be gotten out of a system that undergoes an irreversible process, as compared to a reversible process.

Step-by-Step Solution

Answer

Statement A: True. All spontaneous processes are irreversible as they lead to an increase in entropy and cannot be simply reversed without external input. Statement B: True. The entropy of the universe increases for spontaneous processes, as per the second law of thermodynamics. Statement C: False. In an irreversible process, the change in entropy of the surroundings is not equal and opposite in sign to the change in entropy of the system; there is a net increase in entropy overall. Statement D: False. The maximum amount of work can be gotten out of a system that undergoes a reversible process, not an irreversible process. Irreversible processes involve a greater increase in entropy and produce less work than reversible processes.

Step 1: Statement A Analysis

The statement is: "All spontaneous processes are irreversible." We know spontaneous processes occur naturally without any external input, and irreversible processes cannot be undone by simply reversing the process. Are all spontaneous processes irreversible? Let's examine it.

Step 2: Statement A Answer: True

It's true that all spontaneous processes are irreversible. Once a spontaneous process occurs, it cannot simply be reversed to return to its original state without an external influence. This is because spontaneous processes lead to an increase in entropy, and the only way to reverse them would be to decrease entropy, which requires an external input.

Step 3: Statement B Analysis

The statement is: "The entropy of the universe increases for spontaneous processes." Entropy is a measure of disorder or randomness, and the universe's overall entropy is important for understanding spontaneous processes.

Step 4: Statement B Answer: True

It's true that the entropy of the universe increases for spontaneous processes. According to the second law of thermodynamics, the total entropy of a closed system (such as the universe) must always increase or remain the same over time. Since spontaneous processes involve an increase in entropy, the entropy of the universe also increases in these processes.

Step 5: Statement C Analysis

The statement is: "The change in entropy of the surroundings is equal in magnitude and opposite in sign for the change in entropy of the system, for an irreversible process." We need to analyze if this is true for irreversible processes.

Step 6: Statement C Answer: False

This statement is false. In an irreversible process, the change in entropy of the surroundings is not equal and opposite in sign to the change in entropy of the system. In fact, for irreversible processes, the total entropy change of the universe (system + surroundings) is greater than zero, meaning there is a net increase in entropy overall.

Step 7: Statement D Analysis

The statement is: "The maximum amount of work can be gotten out of a system that undergoes an irreversible process, as compared to a reversible process." To answer this, we must examine the difference between the two processes and their relationship with work output.

Step 8: Statement D Answer: False

This statement is false. A reversible process is an ideal process that will generate the maximum amount of work from a system. In a reversible process, the system is always in equilibrium with its surroundings, allowing it to generate the most work out of a given amount of heat. In contrast, an irreversible process involves a greater increase in entropy, meaning it will produce less work than a reversible process.

Key Concepts

Second Law of Thermodynamics

The second law of thermodynamics is a fundamental principle that governs the direction of thermal processes. It reveals the natural tendency towards disorder in the universe. This law states that the total entropy, or disorder, in a closed system will either increase or remain constant over time, but it will never decrease on its own.

The concept of entropy relates to the dispersal of energy: when energy is uniformly distributed within a system, the entropy is high. In contrast, low entropy suggests a system that has pockets of concentrated energy. According to the second law, spontaneous processes—those that happen naturally without being driven—always lead to an increase in the overall entropy of the system plus its surroundings.

This key concept has massive implications in various fields, from engineering to cosmology, as it limits the efficiency of heat engines and predicts the ultimate fate of the universe.

Irreversible Process

An irreversible process is one that cannot be undone by simply reversing the steps. Such a process usually involves an increase in entropy and often includes phenomena like friction, turbulence, and inelastic deformation. Due to these factors, when attempting to reverse an irreversible process, additional work must be done or heat must be added, which inevitably leads to an even greater increase in entropy.

In contrast to a reversible process, an irreversible one is characterized by a net positive increase in the entropy of the universe. This aligns with the notion that entropy tends to increase, making irreversible processes more common in nature. When we factor in their spontaneous nature and inability to be undone cleanly, it becomes clear why these processes are much more prevalent than their reversible counterparts.

Reversible Process

Now let's address a reversible process, which is a much more idealized concept in thermodynamics. A reversible process is an ideal process that can be reversed without leaving any trace that it occurred; no change in the universe occurs. These processes are characterized by being infinitely slow, ensuring the system is in a state of equilibrium with its surroundings at all times.

Reversible processes often serve as a benchmark for determining the maximum potential work that a system can perform. For educational purposes, they provide a useful comparison against real-world irreversible processes and, consequentially, demonstrate the inherent inefficiencies present in practical applications due to factors like friction and heat loss.

Work and Thermodynamics

The relationship between work and thermodynamics is particularly crucial when discussing energy conversion and efficiency. In thermodynamics, 'work' refers to the energy transferred when a force is applied over a distance. This concept is closely tied to the first law of thermodynamics which deals with the conservation of energy.

The second law, on the other hand, places a restriction on the amount of work that can be extracted from a system. While a reversible process, being an ideal scenario, can theoretically yield the maximum possible work, real-life processes are irreversible and produce less work due to the increase in entropy. Thus, understanding this relationship is essential for engineers designing practical systems such as engines or refrigerators, where maximizing work output while minimizing energy input is often the goal.