Part of the evidence for restricted rotation about the carbon-nitrogen bond in a peptide linkage comes from 1H NMR studies done with simple amides. For example, at room temperature the 1H NMR spectrum of N, N-dimethylformamide, (CH3)2NCHO, shows a doublet at d 2.80 (3H), a doublet at d 2.95 (3H), and a multiplet at d 8.05 (1H). When the spectrum is determined at lower magnetic field strength the doublets are found to have shifted so that the distance (in hertz) that separates one doublet from the other is smaller. When the temperature at which the spectrum is determined is raised, the doublets persist until a temperature of 111 °C is reached; then the doublets coalesce to become a single signal. Explain in detail how these observations are consistent with the existence of a relatively large barrier to rotation about the carbon-nitrogen bond of DMF.