Question

Indicate whether each statement is true or false. (a) If a system undergoes a reversible process, the entropy of the universe increases. (b) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (c) If a system undergoes a reversible process, the entropy change of the system must be zero. (d) Most spontaneous processes in nature are reversible.

Short answer

(a) False - The entropy of the universe remains unchanged for a reversible process. (b) True - The change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings during a reversible process. (c) False - The entropy change of the system is not necessarily zero, but is matched by an equal and opposite change in the surroundings. (d) False - Most spontaneous processes in nature are irreversible.

Step-by-step solution

Statement a: True or False?

If a system undergoes a reversible process, the entropy of the universe increases. This statement is false. For a reversible process, the entropy of the system must be zero, meaning there will be no change in entropy. If there is no entropy change of the system, the entropy change of the surroundings must also be zero. Therefore, the total entropy of the universe remains unchanged.

Statement b: True or False?

If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. This statement is true. For a reversible process, the change in entropy of the system is matched by an equal and opposite change in the entropy of surroundings. A reversible process ensures that the combined entropy of the system and surroundings remains constant.

Statement c: True or False?

If a system undergoes a reversible process, the entropy change of the system must be zero. This statement is false. Under a reversible process, the entropy change of the system is not necessarily zero; it just means that it's matched by an equal and opposite change in the surroundings. In other words, during a reversible process, any increase in entropy of the system will be matched by a decrease in entropy of the surroundings, and vice versa.

Statement d: True or False?

Most spontaneous processes in nature are reversible. This statement is false. In reality, most spontaneous processes in nature are irreversible because they involve some loss of energy to the surroundings in the form of heat, making it impossible to return to the original state without external intervention. In summary: (a) False (b) True (c) False (d) False

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In essence, it studies how energy is converted from one form to another and how it affects matter. This field is fundamental to our understanding of physical phenomena and underlies many scientific and engineering applications.

It encompasses several laws, which describe the flow of energy and how energy interacts with systems. When we delve into the realms of engines, refrigerators, and even biological systems, we are observing thermodynamics in action. The efficiency of machines, the flow of heat in our atmosphere, and even the workings of stars can be understood through thermodynamic principles.

Learning about thermodynamics lets us comprehend not just simple energy conservation, but also the intricacies of how work and heat transfer happen at microscopic and macroscopic levels.

Second Law of Thermodynamics

The second law of thermodynamics is a fundamental principle which asserts that entropy, a measure of disorder or randomness, in an isolated system can never decrease over time. This law brings the concept of irreversibility to the forefront of physics. It implies that natural processes tend to move towards a state of equilibrium and increased entropy.

Entropy and the Second Law

In simple terms, the second law means that without external work being done, heat will flow from a hot object to a colder one, and not the other way around. It's the reason why we can't convert all the heat from a hot source into work, and why some energy is always 'wasted' or dissipated as heat. The law frames the limitations of energy conversions and the directionality of natural processes.

As a student, understanding the second law can help you fathom why some processes are spontaneous and others are not, and why there's always a certain inefficiency in energy transfer processes.

Spontaneous Processes

A spontaneous process is a physical or chemical change that occurs under a specific set of conditions without any external intervention. It is fundamentally driven by the increase in entropy, as stipulated by the second law of thermodynamics.

Spontaneity doesn't equate to speed; instead, it's about the inherent tendency of a process to proceed. Melting ice, rusting iron, and burning wood are all examples of spontaneous processes. They occur because the state they move towards has greater entropy — is more probable — than the state they're coming from.

In thermodynamic terms, understanding spontaneity is crucial to predicting the direction of a reaction or process. It also has practical implications in designing systems that either facilitate or control these spontaneous reactions, such as chemical reactors or batteries.

Entropy Change

Entropy change is a quantitative measure of the amount of disorder or randomness introduced during a process. In a thermodynamic sense, it is the cornerstone concept in identifying the feasibility and direction of a process.

When a process occurs, if the entropy of a system increases, it is often a sign that the process is spontaneous. However, when we take into account the surroundings as well, the total entropy change, including both the system and its surroundings, must be considered to determine spontaneity. A reversible process, in theory, is characterized by an entropy change of the system that is balanced by an equal and opposite change in the surroundings.

Calculating Entropy Change

Calculating entropy change involves understanding both the quantitative measures of energy transferred as heat and the temperature at which the transfer occurs. The formula \( \Delta S = \frac{q_{rev}}{T} \) is often used, where \( \Delta S \) is the entropy change, \( q_{rev} \) is the heat involved in a reversible process, and T is the absolute temperature. This mathematical approach to entropy allows us to predict and quantify changes in disorder for various processes, thus serving as a valuable tool in both scientific and engineering contexts.