Which of the following represents a relation for ‘heat lost = heat gained?

The relation 'heat lost = heat gained' is the fundamental principle of calorimetry. This principle states that when two bodies of different temperatures are brought into thermal contact in an isolated system, heat energy flows from the hotter body to the colder body until thermal equilibrium is reached. Assuming no heat is lost to the surroundings, the total heat energy lost by the hot body is exactly equal to the total heat energy gained by the cold body. This is also known as the law of mixtures or the law of heat exchange. While thermal equilibrium is the state reached at the end of this process, the specific mathematical equality of heat exchange is defined by calorimetry. Other options like the principle of vaporization specifically concern phase changes rather than general heat exchange.