Chapter 2, Problem 2A.1P

Interpretation Introduction

Interpretation: The molar internal energy of carbon dioxide $\left({\text{CO}}_2\right)$ at $25°\text{C}$ taking into account its rotational and translational degrees of freedom has to be calculated.

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,

    $\Delta U=C_{\text{v}}\Delta T$