### Correct Option: B. The total energy of an isolated system remains constant over time. #### Detailed Explanation: The principle of conservation of energy is a fundamental concept in physics that states that the total energy of an isolated system remains constant over time. This means that energy cannot be created or destroyed; it can only change forms or be transferred between objects within the system. 1. **Understanding Energy**: - Energy exists in various forms, such as kinetic energy (energy of motion), potential energy (stored energy due to position), thermal energy (heat), and many others. - In an isolated system, the sum of all these forms of energy remains constant, even though energy may change from one form to another. 2. **Isolated System**: - An isolated system is one that does not exchange energy or matter with its surroundings. For example, a closed container with gas inside can be considered an isolated system if no heat or work is exchanged with the environment. - In such a system, if the gas expands and does work on the walls of the container, the energy used for that work comes from the internal energy of the gas, but the total energy remains the same. 3. **Mathematical Representation**: - The conservation of energy can be expressed mathematically as: \[ E_{\text{initial}} = E_{\text{final}} \] - This equation implies that the total energy at the beginning of a process (initial) is equal to the total energy at the end of the process (final), accounting for all forms of energy. 4. **Examples**: - A classic example is a pendulum. At its highest point, the pendulum has maximum potential energy and minimum kinetic energy. As it swings down, potential energy converts to kinetic energy, reaching maximum kinetic energy and minimum potential energy at the lowest point. Throughout the swing, the total mechanical energy (potential + kinetic) remains constant, assuming no air resistance or friction. #### Why Other Options Are Incorrect: - **Option A: Energy can be created but not destroyed.** - This statement is incorrect because it contradicts the conservation principle. Energy cannot be created; it can only be transformed from one form to another. For example, chemical energy in fuel is converted to thermal energy when burned, but the total energy remains constant. - **Option C: Energy can be destroyed but not created.** - This option is also incorrect. While it correctly states that energy cannot be created, it wrongly claims that energy can be destroyed. The conservation of energy principle asserts that energy can neither be created nor destroyed; it can only change forms. - **Option D: Energy can be transferred between systems but never converted into different forms.** - This statement is misleading. While it is true that energy can be transferred between systems, it is also incorrect to say that energy cannot be converted into different forms. In fact, energy conversion is a key aspect of the conservation of energy principle. For example, electrical energy can be converted into light energy in a light bulb. ### Revision Summary: - The principle of conservation of energy states that the total energy of an isolated system remains constant over time. - Energy can change forms (e.g., kinetic to potential) but cannot be created or destroyed. - An isolated system does not exchange energy or matter with its surroundings. - Understanding energy transformations is crucial for applying the conservation principle in various physical scenarios.