A system has \(60 \mathrm{~J}\) of heat added to it, resulting in \(15 \mathrm{~J}\) of work being done by the system and exhausting the remaining \(45 \mathrm{~J}\) of heat. What is the efficiency of this process? A. \(100 \%\) B. \(60 \%\) C. \(45 \%\) D. \(25 \%\)

In thermodynamic systems, 'work output' refers to the useful work that is generated by a system during a process. It is generally measured in Joules (J) and can be mechanical work, electrical work, or other forms of energy.
When heat energy is added to a system, some of it transforms into useful work while the rest is exhausted as waste heat.
The work output is an essential parameter in determining the efficiency of a system, as it indicates how effectively the system is converting heat energy into usable work.

The 'heat input' in a thermodynamic system is the total amount of heat energy introduced into the system to drive a process. This heat energy is also measured in Joules (J).
In our exercise example, the system received a heat input of 60 J. After some of the heat is converted into work, the rest is usually discarded as waste.
Calculating the heat input correctly is vital as it is used as the denominator in the efficiency formula, which helps determine how efficiently a system converts heat into work.

Energy efficiency is a measure of how well a system converts the input energy into useful work. It's usually expressed as a percentage and is calculated using the formula:
\[\text{Eff} = \frac{W}{Q_{\text{in}}} \times 100\] In this formula, \( W \) is the work output, and \( Q_{\text{in}} \) is the heat input.
For our exercise, we calculated an efficiency of 25%, which tells us that only 25% of the input heat energy is converted into work, while the remaining 75% is lost as waste heat.
High-efficiency systems are more desirable because they make better use of the input energy, resulting in cost savings and reduced waste.

Thermodynamics is a branch of physics that studies energy and heat transfer. It deals with the principles governing the conversion of energy from one form to another. Understanding the fundamental concepts of thermodynamics is essential for solving problems related to energy efficiency.
Key concepts include the first law of thermodynamics, which states that the total energy in a system is conserved: energy can neither be created nor destroyed, only transformed.
In our exercise, we applied this principle to calculate the efficiency of a system by analyzing the heat input and the resulting work output. This helps us understand how effectively the system operates and how much energy is wasted in the process.