In a certain automobile engine, \(17 \%\) of the total energy released in burning gasoline ends up as mechanical work. What's the engine's mechanical power output if its heat output is \(68 \mathrm{kW} ?\)

The concept of energy conversion efficiency is crucial in understanding how different systems, like automobile engines, transform one form of energy into another. This term specifically refers to the ratio of useful energy output to the total energy input. In the context of the exercise, only 17% of the total energy from burning gasoline is converted into mechanical work, with the remainder mostly lost as thermal energy.

To improve comprehension of this concept, think of energy efficiency as a measure of a system's ability to perform its intended task without wasting energy. High-efficiency systems waste less energy, highlighting their importance in both economics and environmental conservation.

When discussing thermal energy, we're referring to the internal energy present in a system due to the kinetic energy of its molecules. In many engines, like the one described in the exercise, thermal energy is the primary form of energy loss. As gasoline combusts to drive the engine, not all the released energy can be directed to mechanical work. Instead, a significant portion becomes thermal energy which is often released into the environment.

Students should visualize thermal energy as the byproduct of every energy conversion process and recognize its implications for efficiency and system design.

The work-energy principle tells us that the work done by the forces acting on an object results in a change in the kinetic energy of that object. In the context of an engine, the work is the mechanical output – the force exerted by the engine to move the vehicle. This is directly tied to the engine's energy conversion efficiency.

Understanding this principle can help students relate the mechanical work—what's actually powering the car—to the amount of fuel energy consumed. As only a fraction of fuel energy is converted into work, the work-energy principle offers a foundation for improving engine designs to maximize the mechanical work obtained from fuel.

To calculate power, which is the rate at which work is done or energy is transformed, the work-energy principle is applied over time. Power is measured in watts (W), and in our exercise, it's the mechanical power output we're interested in. Knowing the heat energy output and efficiency, we can deduce the overall energy input and then calculate the power output responsible for doing mechanical work.

In practical terms, if an engine's heat output is 68 kW and this represents 83% of the total energy due to efficiency losses, one can determine the actual mechanical power output by considering the remaining 17%. This application connects the abstract concepts of work and energy to the more tangible measurement of mechanical power, something that students can relate to real-world engine performance.