text: For a statistical ensemble, this quantity is equal to the "variance in energy, over Boltzmann's constant, times temperature squared.
full_question: For a statistical ensemble, this quantity is equal to the "variance in energy, over Boltzmann's constant, times temperature squared." One model of this quantity predicted its cubic dependence at low temperatures by modelling vibrations as phonons. At higher temperatures, this quantity is proportional to the molar mass of metal solids with a ratio of roughly 3 times the ideal gas constant. The derivative of internal energy with respect to temperature gives this quantity at constant volume. This quantity, which is modeled by the Dulong-Petit and Debye models has a value of 4.184 joules per gram Celsius for water. For 10 points, name this amount of heat needed to change the temperature of a material.
first_sentence: For a statistical ensemble, this quantity is equal to the "variance in energy, over Boltzmann's constant, times temperature squared.
raw_answer: heat capacity [or specific heat capacity; or molar heat capacity]