Next, we consider the average energy of the harmonic oscillator at fixed . Note that the deviation of classical from quantum behavior is reduced as the frequency, and hence the energy gap between quantum states, is reduced. In the early twentieth century, experimentally measured values of the heat capacity for solids at low temperature, which can be approximated as three dimensional arrays of harmonic oscillators, pointed to a problem in the classical theory. The frequency dependencies of U and at 300 K are shown in the second figure. Again, the values have been scaled by a factor of 1500.
Water can absorb and release considerable thermal energy with little change in temperature.
Hence, average coastal temperatures are cooler in summer than inland temperatures as the water absorbs and stores heat. The reverse is true in winter, as the water releases the stored energy.