More than 150 years ago Pierre Dulong and A. T. Petit...

More than 150 years ago Pierre Dulong and A. T. Petit discovered a rule of thumb that the heat capacity of one mole of a pure solid element is about 6.0 calories per ${ }^{\circ} \mathrm{C}$ (i.e., about $25 \mathrm{~J} /{ }^{\circ} \mathrm{C}$ ). A $100.2-\mathrm{g}$ sample of an unknown metal at $99.9^{\circ} \mathrm{C}$ is placed in $50.6 \mathrm{~g}$ of water at $24.8^{\circ} \mathrm{C}$. The temperature is $36.6^{\circ} \mathrm{C}$ when the system comes to equilibrium. Assume all heat lost by the metal is absorbed by the water. What is the likely identity of this metal?

Key Concepts

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In calorimetry experiments, the heat lost by one substance is equal to the heat gained by another, and this balance is used to determine unknown quantities such as specific heat capacity.

Thermal Equilibrium

Thermal equilibrium is the state reached when two or more systems or substances that are initially at different temperatures come into contact and exchange heat until they reach the same temperature. In many experiments, the final temperature is used to calculate unknown thermal properties of a material once equilibrium is established.

Specific Heat Capacity

Specific heat capacity is a property that indicates the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. This concept is crucial in calorimetry because it allows for the calculation of heat transfer between substances undergoing temperature changes.

Calorimetry

Calorimetry is the experimental technique used to measure the amount of heat involved in a chemical or physical process. It relies on monitoring temperature changes in a system and applying energy conservation principles to determine properties like specific heat or enthalpy changes.

Dulong-Petit Law

The Dulong-Petit law is an empirical rule stating that the molar heat capacities of many solid elements are approximately constant, around 25 J/(°C·mol). This rule of thumb provides a way to estimate the molar mass of a metal based on its measured specific heat capacity, linking microscopic properties to thermodynamic behavior.

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