Question

How does useful work differ from actual work? For what kind of systems are these two identical?

Short answer

" The difference between useful work and actual work lies in their context. Useful work refers to the portion of energy in a system that is effectively utilized for achieving the desired outcome, while actual work considers the total energy supplied to the system, including waste and losses. These two concepts are identical in perfectly efficient systems, where there are no energy losses or waste. However, perfect efficiency is usually unachievable in real-world scenarios, making these two concepts different in most cases.

Step-by-step solution

1. Define useful work

Useful work refers to the amount of work or energy transferred to a system that is converted into a desired or useful outcome. This typically includes the energy needed to overcome friction, move objects, or power machinery. Useful work is often a measure of the efficiency of a system, since it indicates the amount of energy actually used for achieving the desired results.

2. Define actual work

Actual work is the total amount of work or energy transferred to a system, regardless of whether it is used for a useful purpose or not. This includes not only the useful work but also any losses in the system, such as heat, noise, or energy consumed by inefficiencies in the form of friction or other waste.

3. Difference between useful work and actual work

The primary difference between useful work and actual work lies in their context. Useful work focuses on the amount of energy that is effectively utilized for achieving the desired outcome in a system, while actual work includes all the energy supplied to the system, including waste and losses. In other words, actual work considers the total input energy, whereas useful work focuses on the portion of that energy that contributes to the desired result.

4. Identifying systems where useful work and actual work are identical

Useful work and actual work are identical in systems that are perfectly efficient, meaning there are no energy losses or waste in the conversion process. These systems are often theoretical or hypothetical, as perfect efficiency is generally not achievable in real-world scenarios. For instance, a theoretical frictionless machine or a system with 100% conversion efficiency would have identical useful and actual work. However, in most real-world scenarios, energy is lost in the form of heat, friction, or other forms of waste, making the two concepts different from one another.