Einstein Solid Heat Capacity
Watch quantized lattice modes suppress a solid's heat capacity.
Free theory articleWatch quantized lattice modes suppress a solid's heat capacity.
Concept & interpretation
In 1907, Albert Einstein proposed a model to explain the low-temperature deviation of the heat capacity of solids from the classical Dulong-Petit law. The Einstein solid models a lattice of N atoms as 3N independent quantum harmonic oscillators, all vibrating at the same frequency ω.
Native experiment
Open Einstein Solid Heat Capacity to explore how the heat capacity responds to different reduced temperatures.
- Set Reduced temperature to 5. Notice that the Heat capacity ratio is very close to 1 (about 0.9967), approaching the classical Dulong-Petit limit.
- Set Reduced temperature to 0.5. The Heat capacity ratio drops significantly to roughly 0.724, showing the beginning of quantum suppression.
- Set Reduced temperature to 0.1. The Heat capacity ratio plummets to about 0.0045. The modes are "frozen out" because the thermal energy k_B T is much less than the level spacing ℏω.
- Set Reduced temperature to 0. At absolute zero, the Heat capacity ratio is exactly 0 and the quantum capacity deficit is 1.