The principle of conservation of energy asserts that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another.

Energy is a fundamental concept in physics, defined as the capacity to perform work. This principle is rooted in the first law of thermodynamics, which states that the total energy within a closed system remains constant. In essence, this means that while energy may change forms or be transferred, it is never generated or annihilated.

The conservation of energy principle has numerous practical applications in both physics and engineering. For instance, it is instrumental in calculating the energy required for tasks such as lifting weights or moving objects. Furthermore, this principle is crucial in the design of energy-efficient systems like engines and power plants.

Mathematically, the principle of conservation of energy can be expressed with the equation:

In this equation, $\Delta E$ represents the change in energy of a system, $Q$ denotes the heat added to the system, and $W$ indicates the work performed by the system. This relationship highlights how energy is exchanged between a system and its surroundings through heat and work.

In summary, the principle of conservation of energy is a core concept in both physics and engineering. It articulates that energy cannot be created or destroyed, only transferred or transformed. This principle not only underpins theoretical frameworks but also finds extensive practical applications, encapsulated mathematically in the equation $\Delta E = Q - W$.