Question

Consider a process during which no entropy is generated \(\left(S_{\mathrm{gen}}=0\right) .\) Does the exergy destruction for this process have to be zero?

Short answer

Answer: Yes, if there is no entropy generation (S_gen = 0) in a process, the exergy destruction will be zero. This is because the exergy destruction is directly related to entropy generation through the equation, Exergy destruction = T0 × S_gen. If S_gen = 0, then Exergy destruction = 0.

Step-by-step solution

Understand the concept of entropy generation and exergy destruction

Entropy generation is a measure of the irreversibilities in a system. It is caused due to heat transfer, friction, or any other process that causes a deviation from the ideal reversible process. When the entropy generation is zero, it means that the process is reversible. Exergy, on the other hand, is the maximum potential work that can be extracted from a system. Exergy destruction refers to the degradation of this maximum work potential due to irreversibilities in the process. In other words, exergy destruction is a measure of lost work potential.

Correlate entropy generation with exergy destruction

We will use the following relation to connect entropy generation and exergy destruction: Exergy destruction = \(T_0 \times S_{gen}\) where, \(T_0\) = Surrounding temperature \(S_{gen}\) = Entropy generation during a process From the given problem, \(S_{gen} = 0\).

Determine if exergy destruction is zero or not

Substituting the given value of \(S_{gen}\) in the above equation for exergy destruction, we get: Exergy destruction = \(T_0 \times 0\) This simplifies to: Exergy destruction = 0 Therefore, if there is no entropy generation during a process, the exergy destruction for the process is indeed zero.

Key concepts

Entropy Generation

The concept of entropy generation is central to understanding the second law of thermodynamics. It describes the amount of energy that has been irreversibly dissipated as heat, resulting in a loss of useful work potential within a system. Entropy generation occurs in real-world processes due to factors like friction, unrestrained expansion, mixing of different substances, and heat transfer through a finite temperature difference.

Imagine a steam engine: as steam moves through the engine, some energy is always lost due to friction and heat transfer to the surroundings. This energy cannot be converted into work, which is essentially the 'entropy generation'. It is a quantifiable expression of the disorder introduced to the system owing to these irreversible processes. The higher the entropy generation in a system, the farther the system operates from ideal, reversible conditions.

If we improve our steam engine to reduce friction and better insulate it to minimize heat loss, we can decrease entropy generation. This would lead to a more efficient engine with less energy loss, which aligns with the goal of maximizing the work potential of systems in thermodynamics.

Thermodynamics Reversible Process

A thermodynamics reversible process is a conceptual benchmark against which real processes are compared. In an idealized reversible process, a system undergoes changes in such a manner that the system and its surroundings can be returned to their original states without leaving any trace on the universe. That means no entropy is generated, and no exergy is destroyed. Real processes are always irreversible to some degree because they involve some entropy generation and exergy destruction due to natural phenomena like friction and heat loss.

For instance, consider a gas compressing within a piston. If the compression happens infinitely slowly to ensure that the gas remains in thermal equilibrium with its surroundings at all times, this process could be deemed reversible. But in reality, achieving such a scenario is impossible; there is always some rapid motion, temperature gradient, or other effects introducing irreversibility.

Understanding reversible processes is essential for engineers and scientists as it sets the ultimate standard for efficiency and the maximum theoretical work that can be obtained from an energetic system. By studying such ideal processes, we can devise ways to make real, irreversible processes more efficient, bringing them closer to this ideal.

Work Potential

Work potential, in the realm of thermodynamics, refers to the maximum useful work that can be obtained from a system as it moves to a state of equilibrium with its surroundings. It's a value that captures how much a system can 'do' before it naturally settles into a less energetic and more disordered state. The term 'exergy' is often used to quantify this potential.

Let's say you have a boulder perched atop a hill. The potential energy of the boulder due to its height and gravity is a form of work potential. If the boulder rolls down the hill, that potential energy can be converted to kinetic energy and then possibly to other useful forms of work. However, if obstacles in the boulder's path, like trees or holes, cause it to slow down or stop, the potential work is not fully utilized – this is analogous to exergy destruction in thermodynamic systems.

Engineers consistently strive to design systems that maximize work potential - from creating more efficient engines that convert more heat into work, to designing better insulated buildings to minimize heat loss. The understanding of work potential is pivotal for advancements in energy systems, contributing to more sustainable solutions and better resource management.