According to the law of conservation of energy in physics, which of the following correctly states how energy behaves in an isolated system?

Introduction / Context:
The law of conservation of energy is one of the most fundamental principles in physics. It applies in mechanics, thermodynamics, electrical systems and even modern quantum physics. This law states that within an isolated system, the total amount of energy remains constant over time, even though energy may change form. Understanding the correct wording of this law is essential for solving many physics problems and for general scientific literacy. This question asks you to choose the statement that accurately expresses the law of conservation of energy.

Given Data / Assumptions:

• We are considering an isolated system, meaning no energy enters or leaves the system boundaries.
• Energy can exist in many forms such as kinetic, potential, thermal, chemical and electrical.
• In physical processes, energy often transforms from one form to another.
• The total energy before and after a process in an isolated system remains the same.

Concept / Approach:
The correct statement of the law of conservation of energy is that energy can neither be created nor destroyed in an isolated system, but it can be transformed from one form to another or transferred between parts of the system. For example, in a falling object, gravitational potential energy is converted into kinetic energy. In an electric heater, electrical energy changes into thermal energy. At every step, if all forms of energy are accounted for, the total remains constant. Any statement suggesting that energy can be created from nothing or destroyed completely contradicts this fundamental law.

Step-by-Step Solution:
Step 1: Recall the standard wording of the law: energy can neither be created nor destroyed, only converted from one form to another.Step 2: Examine option A and see that it matches this standard wording exactly, adding that energy can change from one form to another.Step 3: Look at option B, which is grammatically incorrect and does not clearly express any valid physical law.Step 4: Consider option C, which mentions energy can neither be created or destroyed but then suggests that energy often disappears, which is not correct when all forms are counted.Step 5: Analyse option D, which claims that energy can either be created or destroyed depending on the process, directly violating conservation.Step 6: Conclude that option A correctly states the conservation of energy.

Verification / Alternative check:
Numerous physics experiments and theoretical developments support energy conservation. For instance, in mechanics, the sum of kinetic and potential energies (plus energy lost to heat and sound) remains constant if all contributions are included. In electrical circuits, the power supplied by sources equals the total power dissipated or stored. Even in nuclear reactions, mass energy equivalence through E = m * c^2 ensures that mass lost is balanced by energy released, so the total energy including rest mass remains constant. All these examples align with the idea that energy is neither created from nothing nor destroyed without trace.

Why Other Options Are Wrong:
Option B is grammatically confusing and does not convey the correct meaning of conservation. Option C introduces the idea that energy disappears completely, which is contrary to experiments where careful accounting of all forms shows constant total energy. Option D explicitly states that energy can be created or destroyed, which directly contradicts the conservation law and modern physics, where even apparent violations are resolved by including all forms of energy.

Common Pitfalls:
Students sometimes focus only on mechanical energy and think conservation is violated when friction converts mechanical energy into heat. In reality, if thermal energy is included, the total stays constant. Another mistake is to confuse conservation of energy with conservation of a specific form of energy, such as kinetic energy alone, which may not be conserved in inelastic collisions. To avoid confusion, always remember that the law refers to the total energy of a closed system, not to individual forms separately.

Final Answer:
The law of conservation of energy states that energy can neither be created nor destroyed, but it can change from one form to another in an isolated system.