Final answer:
The correct description of the law of conservation of energy when no work is done is that the sum of the heat within the system and the heat of the surroundings remains zero (qsystem + qsurroundings = 0), indicating that energy is conserved.
Step-by-step explanation:
The law of conservation of energy states that the total energy of an isolated system remains constant if no work is done on the system or by the system. Given that no heat is exchanged with the surroundings (q = 0) for an isolated system, according to the first law of thermodynamics, there would be no change in the system's internal energy.
Thus, the correct statement that describes the law of conservation of energy when no work is done is qsystem + qsurroundings = 0. This demonstrates that the total energy within the system plus the energy in the surroundings does not change, implying it is conserved.