where p 1 and p 2 are the momenta of the two atoms, and q is the deviation of the inter-atomic separation from its equilibrium value. Every degree of freedom in the energy is quadratic and, thus, should contribute 1 ⁄ 2 k B T to the total average energy, and 1 ⁄ 2 k B to the heat capacity. Therefore, the heat capacity of a gas of N diatomic molecules is predicted to be 7 N · 1 ⁄ 2 k B : the momenta p 1 and p 2 contribute three degrees of freedom each, and the extension q contributes the seventh. It follows that the heat capacity of a mole of diatomic molecules with no other degrees of freedom should be ⁠ 7 / 2 ⁠ N A k B = ⁠ 7 / 2 ⁠ R and, thus, the predicted molar heat capacity should be roughly 7 cal/(mol·K). However, the experimental values for molar heat capacities of diatomic gases are typically about 5 cal/(mol·K) and fall to 3 cal/(mol·K) at very low temperatures. This disagreement between the equipartition prediction and the experimental value of the molar heat capacity cannot be explained by using a more complex model of the molecule, since adding more degrees of freedom can only increase the predicted specific heat, not decrease it. This discrepancy was a key piece of evidence showing the need for a quantum theory of matter.