In a closed system where no heat is lost or gained, what equals the heat lost by the hotter substance?

In a closed system where no heat is lost or gained, the principle of conservation of energy applies. This principle states that energy cannot be created or destroyed, only transferred. When two substances at different temperatures interact, heat will flow from the hotter substance to the colder substance until thermal equilibrium is reached.

The heat lost by the hotter substance is equivalent to the heat gained by the colder substance, but since the question asked which value equals the heat lost by the hotter substance specifically, the heat gained by the colder substance matches this description.

Since the heat lost by the hotter substance must equal the heat gained by the colder substance, these two quantities are fundamentally linked; hence, when calculating or discussing thermal exchanges in closed systems, it's important to understand that they balance out perfectly. This scenario exemplifies the first law of thermodynamics, illustrating that the heat lost by one substance must be gained by another in a system with no energy exchange with the environment.