Question

Is a process that is internally reversible and adiabatic necessarily isentropic? Explain.

Short answer

Answer: Yes, a process that is internally reversible and adiabatic is necessarily isentropic, as it fulfills both the requirements of an isentropic process (adiabatic and reversible).

Step-by-step solution

Understand the key terms

1. Internally Reversible: An internally reversible process is a process in which the system remains at equilibrium at every point during the process. It represents the limit of slow, quasi-static operations. 2. Adiabatic: An adiabatic process is a process that occurs without any heat transfer between the system and its surroundings. In other words, no heat enters or exits the system. 3. Isentropic: An isentropic process is an idealized process that is both adiabatic and reversible. Therefore, during an isentropic process, entropy remains constant (\(\Delta S = 0\)).

Analyze the relationship between the terms

To determine if a process that is internally reversible and adiabatic is necessarily isentropic, we need to analyze the connection between these terms. For a process to be isentropic, it must be both adiabatic (no heat transfer) and reversible. If a process is internally reversible and adiabatic, it meets both these criteria.

Conclusion

A process that is internally reversible and adiabatic necessarily fulfills both the requirements of an isentropic process. Therefore, a process that is internally reversible and adiabatic is indeed necessarily isentropic.

Key concepts

Internally Reversible Process

An internally reversible process is a key concept in thermodynamics that describes a theoretical condition where every stage of the process can be exactly reversed without increasing entropy in the universe. In simple terms, it's like watching a movie of a system's changes played forwards or backwards, and not being able to tell the difference. The system always stays perfectly balanced, or in equilibrium, throughout the transformation.

In practical terms, this is an idealized concept. Real processes always involve some degree of irreversibility due to friction, turbulence, or other forms of energy dissipation. However, picturing a process as internally reversible helps in understanding the fundamental limits and efficiencies of thermal systems. To make the concept clearer, think of pushing a piston in a cylinder very slowly such that the pressure inside can adjust evenly without causing any turbulence or shocks—this is an attempt to approach an internally reversible process.

Adiabatic Process

The notion of an adiabatic process is another cornerstone in thermodynamics representing a process where no heat is exchanged with the surroundings. It’s the thermal equivalent of saying 'what happens in the system, stays in the system'. Imagine a perfectly insulated container; it doesn't let any heat escape or enter—it’s adiabatic.

For students, a useful memory aid is to associate adiabatic with 'adios' to heat transfer. When dealing with real-world problems involving adiabatic conditions, assumptions of perfect insulation are made to simplify the calculations. For instance, rapid processes, where there is no time for heat transfer, are often approximated as adiabatic, such as the compression stroke in an internal combustion engine. Visualizing these hypothetical scenarios can greatly improve one's grasp of energy conservation principles under adiabatic constraints.

Entropy

In the realm of thermodynamics, entropy is a measure often referred to as the 'currency' of energy transactions. It quantifies the level of disorder or randomness within a system. To translate this into everyday language, consider a tidy room (low entropy) and how it naturally tends to become messy over time (high entropy) without effort to maintain order.

Entropy isn't just about cleanliness or messiness; it applies to energy spread within a system as well. When energy is spread out evenly, entropy is high; when it's concentrated, entropy is low. The second law of thermodynamics, regarded as a universal principle, tells us that the entropy of the universe always tends to increase in natural processes. This means that in order to 'pick up the toys and tidy the room'—to decrease entropy in one place—work must be done, and overall, the universe’s entropy will still go up. This perpetual increase in disorder is a fundamental concept that not only underlies the direction of time but also dictates the efficiency of energy conversion processes.