Question

Answer the following true or false. If false, explain why. A process that violates the second law of thermodynamics violates the first law of thermodynamics. (b) When a net amount of work is done on a closed system undergoing an internally reversible process, a net heat transfer of energy from the system also occurs. (c) One corollary of the second law of thermodynamics states that the change in entropy of a closed system must be greater than zero or equal to zero. (d) A closed system can experience an increase in entropy only when irreversibilities are present within the system during the process. (e) Entropy is produced in every internally reversible process of a closed system. (f) In an adiabatic and internally reversible process of a closed system, the entropy remains constant. (g) The energy of an isolated system must remain constant, but the entropy can only decrease.

Short answer

a) False. b) False. c) True. d) False. e) False. f) True. g) False.

Step-by-step solution

- Analyze statement (a)

The second law of thermodynamics states that entropy of an isolated system always increases over time. The first law of thermodynamics states that energy cannot be created or destroyed. A process that violates the second law does not necessarily violate the first law. Therefore, the statement is false.

- Analyze statement (b)

For a closed system undergoing an internally reversible process, net work done on the system implies a change in energy, which could result in heat transfer. However, a net heat transfer out of the system is not a requirement, making the statement false.

- Analyze statement (c)

One corollary of the second law of thermodynamics does indeed state that the change in entropy of a closed system must be greater than or equal to zero. Hence, this statement is true.

- Analyze statement (d)

Entropies in closed systems can increase due to heat transferred into the system even in the absence of irreversibilities. Thus, this statement is false.

- Analyze statement (e)

In internally reversible processes, entropy is conserved and not produced. Therefore, the statement is false.

- Analyze statement (f)

During an adiabatic, internally reversible process, no heat is transferred, and entropy remains constant. Thus, this statement is true.

- Analyze statement (g)

The energy of an isolated system must remain constant, but the entropy can only increase or remain constant as per the second law. Therefore, the statement is false.

Key concepts

Second Law of Thermodynamics

The second law of thermodynamics is a fundamental principle describing how energy transitions occur in isolated systems. It states that in any natural thermodynamic process, the total entropy of an isolated system will either increase or remain constant over time—it never decreases.
Entropy, which is a measure of the disorder or randomness in a system, dictates that energy transformations have a preferred direction. This law explains why certain processes, such as heat spontaneously flowing from a hot object to a cold one, occur naturally.
Some points to remember about the second law of thermodynamics:

• This law is crucial for understanding processes like heat engines and refrigerators.
• While energy remains constant due to the first law, entropy ensures that energy transforms in a specific direction.
• It indicates that perpetual motion machines of the second kind are impossible due to an inevitable increase in entropy.

In essence, the second law describes a tendency towards equilibrium and the natural progression towards increased entropy.

First Law of Thermodynamics

The first law of thermodynamics is synonymous with the principle of conservation of energy. It states that energy cannot be created or destroyed, only transformed from one form to another. The mathematical representation of this law is: \[ \Delta U = Q - W \] where:

• \( \Delta U \): Change in internal energy of the system
• \( Q \): Heat added to the system
• \( W \): Work done by the system

This principle is important for many applications, such as calculating the energy balance in engines, refrigerators, and various other systems.
Some key aspects of the first law of thermodynamics include:

• Energy can change forms, such as from potential energy to kinetic energy or thermal energy.
• In closed systems, where no mass enters or leaves, the total energy remains constant.
• This law forms the foundation for all energy analysis in thermodynamics.

Essentially, the first law underscores that the combined energy within an isolated system remains constant, thereby setting a groundwork for analyzing energy transformations and exchanges.

Entropy Change

Entropy is a central concept in thermodynamics, representing the degree of disorder or randomness in a system. The change in entropy gives insight into the direction and feasibility of thermodynamic processes. The second law of thermodynamics comes into play here, highlighting that for any spontaneous process, the total entropy of a system and its surroundings always increases.
Entropy changes can be understood as follows:

• In an irreversible process, the system's entropy increases because of internal irreversibilities like friction or unrestrained expansion.
• During a reversible process, entropy change can be calculated using the formula: \[ \Delta S = \int \frac{dQ_{rev}}{T} \] where \( \Delta S \) is the change in entropy, \( dQ_{rev} \) represents the infinitesimal heat added reversibly, and \( T \) is the temperature.
• Entropy can remain constant in an adiabatic reversible process, as no heat transfer occurs (adiabatic) and no irreversibilities are present.

Clarifying these aspects, entropy change helps in understanding the efficiency and limitations of various thermodynamic cycles, processes, and systems. It's a key factor in determining whether a process can occur naturally and what the potential impact on energy distribution will be.