Chapter 2, Problem 2E.1BE

Interpretation Introduction

Interpretation: The value of $\gamma$ for carbon dioxide has to be calculated using equipartition principle.  The calculation has to be done with and without the vibrational contribution to the energy.  The value closer to the experimental value at $25°\text{C}$ has to be stated.

Concept introduction: The equipartition theorem states that the energy for a molecule is the combination of energy values for all modes of motion.  This means that the total energy is the sum of translational, vibrational and rotational energy.  The change in internal energy, $\Delta U$, at constant volume is known as heat capacity at constant volume. It is denoted by $C_{\text{v}}$.  The relation between $\Delta U$ and $C_{\text{v}}$ is given by the formula as,

    $\Delta U=C_{\text{v}}\Delta T$