Physics

Physics

Problem

Two samples of liquid water are mixed in an insulated beaker: 100 g100\,\text{g} at 75∘C75^\circ\text{C} and 200 g200\,\text{g} at 25∘C25^\circ\text{C}. In which direction will energy be transferred as heat, and how will the temperatures of the two samples change over time? Answer in one or two sentences.
Intuitive explanation

This is a thermal equilibrium problem where you're applying conservation of energy: the hotter sample loses heat to the cooler one until both reach the same final temperature. The key insight is that the total thermal energy is conserved in an insulated system, so the heat lost by the hot water equals the heat gained by the cold water—use Q=mcΔTQ = mc\Delta T for each sample and set them equal to find where they meet.

Intuitive explanation

This is a thermal equilibrium problem where you're applying conservation of energy: the hotter sample loses heat to the cooler one until both reach the same final temperature. The key insight is that the total thermal energy is conserved in an insulated system, so the heat lost by the hot water equals the heat gained by the cold water—use Q=mcΔTQ = mc\Delta T for each sample and set them equal to find where they meet.

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