Question

Consider a cogeneration plant for which the utilization factor is \(0.5 .\) Can the exergy destruction associated with this plant be zero? If yes, under what conditions?

Short answer

Answer: In theory, a cogeneration plant with a utilization factor of 0.5 can have zero exergy destruction under ideal conditions. However, such a situation is practically unattainable in real-world applications due to inevitable irreversibilities and energy losses present in any energy conversion process. For zero exergy destruction to occur, the plant would need to operate with no irreversibilities, using the most efficient equipment and optimal operating conditions, and its internal processes must be entirely reversible.

Step-by-step solution

Define utilization factor and exergy destruction

Utilization factor is the ratio of the actual useful energy output from a cogeneration plant to the ideal useful energy output. In this exercise, the utilization factor is given as 0.5, which means that the plant is only providing 50% of its potential useful output. Exergy destruction is the energy loss due to irreversibilities in a process. It is the difference between the initial exergy (the maximum work that the system could potentially provide) and the final exergy (the actual work that the system provides).

Analyze the relationship between utilization factor and exergy destruction

The utilization factor gives us important information about the efficiency of the cogeneration plant. A high utilization factor means that the plant is operating efficiently and producing more useful energy output, which results in lower exergy destruction due to fewer irreversibilities. On the other hand, a low utilization factor means that the plant is operating less efficiently and producing less useful energy output, which results in higher exergy destruction due to more irreversibilities.

Determine if exergy destruction can be zero

In the case of a cogeneration plant with a utilization factor of 0.5, this means that the plant is only operating at 50% of its potential useful output. The remaining 50% of the potential output is not being utilized and may be lost due to irreversibilities. However, it does not necessarily mean that the exergy destruction must be nonzero. In order to have zero exergy destruction, the plant would need to operate with no irreversibilities or energy losses, meaning that all of the energy input to the plant is transformed into useful output. Mathematically, this would mean that the exergy efficiency of the plant is 100%.

Identify the conditions for zero exergy destruction

It's important to note that having a zero exergy destruction in a real-world cogeneration plant is practically impossible, due to the presence of various unavoidable irreversibilities, such as friction, heat transfer, and other losses. However, in a theoretical scenario, for the exergy destruction to be zero, the cogeneration plant would need to operate under ideal conditions and have the following properties: 1. The plant must be designed and operated in such a way that it minimizes any energy losses and irreversibilities. This would require the use of the most efficient equipment and optimal operating conditions. 2. The internal processes and energy transformations within the plant must be entirely reversible, meaning that no energy is lost or dissipated in any form. In conclusion, while it is theoretically possible for a cogeneration plant with a utilization factor of 0.5 to have zero exergy destruction under ideal conditions, such a situation is practically unattainable in real-world applications due to inevitable irreversibilities and energy losses that are present in any energy conversion process.