How do energy and work relate in a closed system?

In a closed system, work done is equal to the change in energy of the system.

In physics, a closed system is one where neither matter nor energy can enter or leave. The total energy within a closed system is always conserved. This principle is known as the conservation of energy. When work is done on or by the system, it results in a change in the system's energy.

Work is a way of transferring energy from one system or object to another. It is defined as the force applied to an object multiplied by the distance over which it is applied, and it is measured in joules, the same unit as energy. When work is done on a system, energy is transferred into the system, increasing its total energy. Conversely, when a system does work on its surroundings, energy is transferred out of the system, decreasing its total energy.

In a closed system, any work done must result in a corresponding change in the system's energy. If work is done on the system, its energy increases; if the system does work, its energy decreases. This is because in a closed system, energy cannot be created or destroyed, only transferred or transformed.

For example, consider a car accelerating along a flat road. The engine does work on the car, causing it to speed up. This work is transferred into kinetic energy, increasing the total energy of the car. If the car then slows down, it does work on the brakes, transferring energy out of the system and decreasing its total energy.

In summary, work and energy are intimately related in a closed system. Work represents a transfer or transformation of energy, and the total energy of the system changes by an amount equal to the work done. This relationship is a direct consequence of the conservation of energy, a fundamental principle in physics.