Physics

Problem

An energy input of

9.0\,\text{kJ}

raises the temperature of

0.30\,\text{kg}

of iron (specific heat

450\,\text{J}\,kg^{-1}\,^{\circ}\text{C}^{-1}

) by

67\,^{\circ}\text{C}

. The same

9.0\,\text{kJ}

of energy is delivered to a sample of aluminum (specific heat

900\,\text{J}\,kg^{-1}\,^{\circ}\text{C}^{-1}

) that starts at the same initial temperature. Determine the mass of aluminum that will experience the same

67\,^{\circ}\text{C}

temperature rise.

Intuitive explanation

This problem tests your understanding of how specific heat capacity determines how much a material's temperature changes for a given energy input. The key insight is that the same heat energy $Q$ produces different temperature rises in different materials—but here you're asked to find the mass of aluminum that gives the same rise as the iron. Use the heat equation $Q = mc\Delta T$ to set up a ratio: since both samples receive the same energy and experience the same temperature change, the ratio of their masses must be inversely proportional to the ratio of their specific heats.

Intuitive explanation

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