Debye temperature and Frenkel temperature of liquid water at atmospheric pressure are estimated from the modified phonon-polariton model. Moreover, the decrease in the Debye temperature and the increase in the Frenkel temperature as rising temperature are pointed out. The heat capacity of liquid water is given by the phonon theory reported in 2012, covering both classical to quantum regimes for both the motion of phonon polariton and the di˙usion motion of particles. Because the ratio between temperature and the Debye temperature varies from 0.8 to 1.5, leading to the temperature independence of the heat capacity of liquid water at atmospheric pressure, in agreement with experimental work.

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