Balarin [1,2] deduced some expressions for determining the activation energy, based on the quantity ?=T ₂ ? T ₁ , where T ₁ and T ₂ correspond to the temperatures on either side of T _M , corresponding to half intensity. In the following the Balarin s original symbolism is used.

He started from the following general rate equation

(1)

with and where

• c=concentration of some kind of reactant,

• ?=kinetic order,

• k ₀=frequency factor,

• E=activation energy,

• ?=time,

• T=temperature,

• k=Boltzmann constant.

The processes governed by Eq.(1) are enhanced when the temperature of the system is raised continuously with a constant heating rate . Equation (1) can then be transformed as

(2)

The maximum condition is then obtained

(3)

Considering the following quantities:

Eq.(2) becomes

(4)

Integration of Eq.(4), starting at t=0, T= 0, y=0 and C ₀=1 up to C(T), gives, for various values of ?:

(5)

where

(6)

is a correction function which is always close to unity, ?(y) ?1.

Using expression (6) in (5), we obtain

(7)

(8)

The temperature positions T _i= T ₁ and T ₂ are obtained when the intensity is half of the maximum intensity. By means of Eq.(1) or (4), we get

(9)

where the subscript ( ?) indicates the individual solution for every distinct kinetic order.

Inserting (8) in (9), expressions...