The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of R.

Verified step by step guidance

1. Identify the degrees of freedom for graphene. Since graphene is a two-dimensional material, consider only the translational and vibrational modes in the plane of the sheet.
2. Apply the equipartition theorem, which states that each degree of freedom contributes \(\frac{1}{2}R\) to the molar specific heat, where R is the gas constant.
3. Count the degrees of freedom for each atom in the graphene sheet. Each carbon atom in graphene contributes two translational degrees of freedom (in-plane movements) and potentially two vibrational degrees (in-plane vibrations).
4. Calculate the total molar specific heat by summing the contributions from all degrees of freedom. Since each degree of freedom contributes \(\frac{1}{2}R\), multiply the total number of degrees of freedom by \(\frac{1}{2}R\).
5. Express the final result as a multiple of R, based on the total number of degrees of freedom calculated in the previous steps.

Key Concepts

Graphene Structure

Graphene is a single layer of carbon atoms arranged in a two-dimensional honeycomb lattice. This unique structure gives graphene remarkable mechanical, electrical, and thermal properties, making it a subject of extensive research in materials science and physics.

Molar Specific Heat

Molar specific heat is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. For solids, this value can vary based on the material's structure and bonding, and it is often expressed as a multiple of the universal gas constant, R.

Debye Model

The Debye model is a theoretical approach used to estimate the specific heat of solids at low temperatures. It considers the contributions of phonons (quantized sound waves) to the heat capacity, which is particularly relevant for materials like graphene that exhibit unique vibrational modes due to their two-dimensional structure.