Final answer:
The law of conservation of energy states that the total energy of a closed system remains constant over time. This includes both mechanical and thermal energies, where mechanical energy is the sum of kinetic and potential energy, and is conserved in the absence of external forces. The first law of thermodynamics encompasses this principle through the statement that the change in internal energy of a system is equal to the heat added to the system plus the work done on it. So the correct option is A.
Step-by-step explanation:
The law of conservation of energy in a closed physical system indicates that the total energy within the system remains constant over time. This concept is articulated in the question which concerns how mechanical and thermal energies are conserved within such a system. To clarify, none of the answer choices directly match the principles of energy conservation as generally understood in physics. However, using the information provided, we can explore the principles relevant to the question.
In a closed system, mechanical energy, which includes both kinetic and potential energy, is conserved unless acted upon by external forces. If a piston does work (W), it may convert some of the system's internal energy to kinetic energy, but the total mechanical energy of the system will not change. This aligns with the principle that during any process, the change in a system's mechanical energy will be equal to the work done on the system minus any heat transfer (Q).
According to the first law of thermodynamics, the change in internal energy of a system (ΔE) is equal to the heat added to the system (Q) plus the work done on the system (W). This statement encompasses the conservation of thermal energy as part of the system's total energy. The energy may shift between mechanical and thermal forms, but the total remains the same.
Therefore, the interpretation of the law of conservation of energy should reflect these ideas, and none of the answer choices provided perfectly do so. The closest is perhaps option A, which mentions the transfer of mechanical energy and the work done by the piston, but the phrasing about energy differences is not accurate.