Volumetric heat capacity, exponential function of T + Gaussian of T

Presentation

This model defines a volumetric heat capacity ρCp as an exponential function of the temperature, taking the energy of phase transition (Curie point, ...) into consideration.

Mathematical model

The volumetric heat capacity is the combination of an exponential function and a Gaussian function of the temperature.

The corresponding mathematical formula is written:

with

where:

• ρCp₀ is a constant the volumetric heat capacity at T = 0 °C (J/m³/°C)

• ρCp_i is another constant the volumetric heat capacity at T = infinite (J/m³/°C)

• E is the energy of phase transition (J/m³)
• σ is the typical Gaussian standard deviation (°C)
• T_C is the transition temperature (Curie temperature, …) (°C)
• τ is a temperature constant of the exponential function (positive or negative) (°C)

The shape of ρCp(T) curve is presented in the figure below.