Table: 3.

Thermodynamic parameters of madder dye at different heating rate at temperature (100 °C).

S. No.	Heating rate	Stage	Temp.	Ea (kJ mol−1)	ΔS (kJ mol−1)	ΔH (kJ mol−1)	ΔG (kJ mol−1)
1	10 °C/min.	1	100	43.7170	−0.1590	40.6158	99.9267
2	20 °C/min.	1	100	56.0500	−0.1291	52.9488	101.0891
3	30 °C/min.	1	100	14.5698	−0.2472	11.4686	103.6714
4	40 °C/min.	1	100	24.9283	−0.2317	21.8271	108.2486
5	50 °C/min.	1	100	13.9770	−0.2484	10.8758	103.5327

Thermodynamic parameters at 250 °C are shown in Table 4. The positive ΔG values are appeared in the range from 143.0738 to 152.0953 kJ mol⁻¹ at heating rate 30° and 20° per minute, which confirms the thermally non-spontaneous process. The ΔS negative values are observed in the range from −0.2205 to −0.2777 kJ mol⁻¹ at heating rate 50° and 20° per minute respectively. The positive ΔH values are obtained in the range from 6.8497 to 28.0477 kJ mol⁻¹ at heating rate from 20° to 50 °C per minute. The maximum and minimum E_a values are obtained of 32.3961 and 11.1980 kJ mol⁻¹ at the heating rate of 50° and 20 °C per minute respectively.