Snapshot 1: degradation curve in a reaction following the Arrhenius and first-order (
) kinetics equations with a linearly rising temperature
Snapshot 2: degradation curve in a reaction following the exponential model and zero-order kinetics (
) with a linearly falling temperature
Snapshot 3: degradation curve in a reaction following the exponential model and half-order kinetics (
) with a sinusoidally oscillating temperature
The kinetic order of a degradation reaction or decay process is defined as the exponent
in the static (isothermal) rate equation
with the boundary condition
in the equation representing the momentary concentration at time
and the initial concentration, respectively, and
, the temperature-dependent rate constant having units consistent with
. When the temperature varies,
and the rate equation's solution, which is more often numerical than analytical, depends on the particulars of the temperature history
. This Demonstration generates
curves for linearly rising, linearly falling, and oscillating (sinusoidal) temperature histories whose parameters you can enter and vary with sliders. You can also enter the order
of the reaction or process in the range from 0. to 2.5 with a slider. Although the model equation for
, we treat this scenario as a special case because of its simplicity.
The temperature dependence of the rate constant
is described by either the Arrhenius equation
are the actual and reference temperatures, respectively, in K,
is the energy of activation, and
the universal gas constant, or the simpler exponential model 
is a constant having
units. One can show that the two models have a considerable range of overlap around the reference temperature
This Demonstration shows the temperature history (top) and the corresponding concentration and concentration decay rate curves (middle and bottom) with the momentary numerical values of
and the concentration decay rate at a time
(which you can choose with a slider) shown as a moving dot on the three plots.
The purpose of this Demonstration is to illustrate how a reaction's kinetic order affects the concentration decay curve under nonisothermal conditions. Therefore, not all the decay and decay rate curves that it can produce necessarily represent an actual physical disintegration or degradation process.
 M. Peleg, M. D. Normand, and M. G. Corradini, "The Arrhenius Equation Revisited," Critical Reviews in Foods Science and Nutrition
2012 pp. 830–851.