A kinetic-based approach in accelerating rate calorimetry with the varying thermal inertia consideration


The accelerating rate calorimetry is a powerful tool for thermal hazard evaluation. However, the existing kinetics approaches ignore the fact that the thermal inertia is varying during the pseudo-adiabatic reaction because of the changing of the sample’s heat capacity and heat loss. To overcome this shortcoming, the expression of the thermal inertia is amended based on the heat balance and transfer in this article. The arithmetic product of the sample’s heat capacity and the amended thermal inertia is obtained by merging the kinetic results of the DSC and ARC data. Then, the data from the ARC are corrected and the more reasonable values of the kinetic parameters are computed based on the varying thermal inertia consideration. With the typical n-order and autocatalytic decomposition experiments under the different sample masses, the validity of the proposed kinetic approach is verified. Meanwhile, the hypotheses of the proposed approach are analyzed and discussed in the end of the article.

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Φ :

Constant thermal inertia

C s :

Heat capacity of the sample (J g−1 K−1)

M s :

Mass of the sample (g)

C b :

Heat capacity of the sample container (J g−1 K−1)

M b :

Mass of the sample container (g)

Φ(T, t):

Varying thermal inertia

P ex :

Heat generation rate of the sample (mW)

P loss :

Heat loss rate of the sample (mW)

α :

Extent of conversion

A, A1, A2 :

Pre-exponential factor (s−1)

E, E1, E2 :

Activation energy (J mol−1)


Temperature (K)

R :

Gas constant (8.314 J mol−1 K−1)

n, n1, n21, n22:

Reaction order

t :

Time (s)

H :

Heat release (J)

T f :

Final temperature of reaction in ARC (K)

T o :

Onset temperature in ARC (K)

N :

Sampling number

β :

Heating rate in DSC experiment (K min−1)

i :

Index of the different heating rate in DSC experiments

A α :

Pre-exponential factor (s−1)

E α :

Activation energy (kJ mol−1)


Kinetic model

T α,i :

Temperature (K)

Δαmin :

Minimum internal of α


Arithmetic product of sample heat capacity and amended thermal inertia


Residual sum of squares


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This work was supported by Zhejiang Provincial Public Welfare Research Program (Grant No. LGF18B030001) and Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY17F010011, LQ15F030003).

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Correspondence to Shuliang Ye.

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Ding, J., Yu, L., Wang, X. et al. A kinetic-based approach in accelerating rate calorimetry with the varying thermal inertia consideration. J Therm Anal Calorim 141, 783–796 (2020). https://doi.org/10.1007/s10973-019-09081-z

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  • Thermal inertia
  • Accelerating rate calorimetry
  • Process safety
  • Thermal kinetics