Physics

Physics

Problem

An aluminum cylinder of mass 0.050 kg0.050\,\text{kg} is heated to 120 ∘C120\,^{\circ}\text{C} and quickly submerged in 0.200 kg0.200\,\text{kg} of water at 25 ∘C25\,^{\circ}\text{C} contained in a thermally insulated cup. Assuming no energy is lost to the surroundings and no phase changes occur, determine the equilibrium temperature of the system. (Specific heats: water 4186 J kg−1 ∘C−14186\,\text{J}\,\text{kg}^{-1}\,^{\circ}\text{C}^{-1}, aluminum 900 J kg−1 ∘C−1900\,\text{J}\,\text{kg}^{-1}\,^{\circ}\text{C}^{-1}.)
Intuitive explanation

This is a calorimetry problem where two objects at different temperatures exchange heat until they reach thermal equilibrium. The key insight is that in an isolated system, the total heat lost by the hot object equals the total heat gained by the cold object—so you can set up an equation where Qlost=QgainedQ_{\text{lost}} = Q_{\text{gained}} and solve for the final temperature that satisfies both sides. Since the cup is insulated, no energy escapes, making this a closed energy balance.

Intuitive explanation

This is a calorimetry problem where two objects at different temperatures exchange heat until they reach thermal equilibrium. The key insight is that in an isolated system, the total heat lost by the hot object equals the total heat gained by the cold object—so you can set up an equation where Qlost=QgainedQ_{\text{lost}} = Q_{\text{gained}} and solve for the final temperature that satisfies both sides. Since the cup is insulated, no energy escapes, making this a closed energy balance.

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