Question

What is the second-law efficiency? How does it differ from the first-law efficiency?

Short answer

Answer: The main difference between the Second-law efficiency and the First-law efficiency is that the Second-law efficiency takes into account the irreversibilities and wasted energy present in a system, while the First-law efficiency is based on the conservation of energy principle and does not consider the irreversibilities.

Step-by-step solution

Introduction to Second-law Efficiency

The Second-law efficiency, also called the exergy efficiency, takes into account the inefficiencies or irreversibilities present in a system due to factors such as friction, heat losses, and chemical reactions. It is defined as the ratio of the useful exergy (the maximum available work from a system) obtained from a process, to the exergy supplied to the process. It can be mathematically represented as: \[ \eta_{II} = \frac{Exergy\: Obtained}{Exergy\: Supplied} \]

Introduction to First-Law Efficiency

The First-law efficiency, also known as the energy efficiency, is based on the conservation of energy principle, and is a measure of how effectively a system converts energy from one form to another. It is defined as the ratio of the useful energy (work or heat) output of a process to the energy input to the process. Mathematically, it can be represented as: \[ \eta_{I} = \frac{Useful\: Energy\: Output}{Energy\: Input} \]

Difference between Second-law and First-law Efficiencies

The main differences between Second-law and First-law efficiencies are: 1. Second-law efficiency takes into account the irreversibilities present in a system, while the First-law efficiency considers only the energy conversion and does not account for irreversibilities. 2. Second-law efficiency is based on the maximum available work (exergy) from a process, while the First-law efficiency is based on the conservation of energy principle. 3. First-law efficiency may approach 100% for an idealized system without irreversibilities, whereas Second-law efficiency can never reach 100% due to the presence of irreversibilities in real-life processes. 4. Second-law efficiency provides a more meaningful evaluation of the system's performance, as it not only takes into account the energy conversion but also the wasted energy due to inefficiencies. In summary, the Second-law efficiency is a more comprehensive performance measure that takes into account the irreversibilities and wasted energy present in a system, while the First-law efficiency is a simpler measure based on the conservation of energy principle and does not consider the irreversibilities.