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 tbumb that the heat capacity of one mole of a pure solid element is about $6.0$ calories per ${ }^{\circ} \mathrm{C}$ (i.e., about $\left.25 \mathrm{~J} /{ }^{\circ} \mathrm{C}\right)$. 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

Dulong-Petit Law

The Dulong-Petit law is an empirical rule stating that the molar heat capacity of many solid elements is approximately constant. This law is used as a reference to compare the experimental heat capacity of a metal sample, which can help in identifying the metal based on deviations or agreements with expected heat capacity values.

Conservation of Energy

This principle states that in an isolated system, energy cannot be created or destroyed but only transferred from one form to another. In thermal processes, such as the mixing of substances at different temperatures, the heat lost by the hotter substance is equal to the heat gained by the cooler substance, allowing for the calculation of unknown quantities based on the energy balance.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius. It is a critical parameter in calculating the amount of heat exchanged during temperature changes in calorimetric experiments.

Calorimetry

Calorimetry is the experimental technique used to measure the amount of heat exchanged in chemical and physical processes. It relies on precise measurements of temperature changes and the known specific heat capacities of substances to determine energy changes, making it a key method for identifying materials based on their thermal properties.

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