// multi-utility computation suite · offline · instant · precise
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sci.phonon-Debye-heat-capacity Calculator
Calculates the Debye model heat capacity C_V = 9NkB(T/θD)³∫₀^(θD/T) x⁴eˣ/(eˣ−1)² dx from Debye temperature θD. Below θD, C_V ∝ T³ (Debye T-cubed law) — diamond (θD = 2,230 K) has very low room-temperature heat capacity of 6.1 J/(mol·K) vs the Dulong-Petit limit of 24.9 J/(mol·K).
Inputs
T K
Thermal state of the substance. Check whether the formula needs Celsius, Fahrenheit, or Kelvin (K = °C + 273.15).
Theta D K
Thermal state of the substance. Check whether the formula needs Celsius, Fahrenheit, or Kelvin (K = °C + 273.15).
N Atoms Mol
Reference formula or conversion factor shown for context.
Results
molar heat capacity Cv (J/mol·K)
The value at the specified point or condition.
Dulong-Petit limit 3nR (J/mol·K)
Sample size or count used in the calculation.
Debye T³ law (low T): Cv (J/mol·K)
Reference formula or conversion factor shown for context.
T/Θ_D ratio
The proportional relationship between two quantities.
Debye 1912: Cv → 12π⁴nR/5·(T/Θ_D)³ at low T
The value at the specified point or condition.
regime
The operating regime — the mode or zone in which the system is currently operating.