Mean kinetic temperature

In the pharmaceutical industry, Mean kinetic temperature (MKT) is a calculated temperature that represents the equivalent thermal effect of temperature variations over time, such that the degradation occurring under fluctuating conditions is equal to that which would occur at a constant MKT value.

The mean kinetic temperature can be expressed as:

$T_K=\frac{\frac{\mathrm{\Delta }H}{R}}{-\ln \left(\frac{t_1{e}^{\left(\frac{-\mathrm{\Delta }H}{R{T}_1}\right)}+t_2{e}^{\left(\frac{-\mathrm{\Delta }H}{R{T}_2}\right)}+\cdots +t_n{e}^{\left(\frac{-\mathrm{\Delta }H}{R{T}_n}\right)}}{t_1+t_2+\cdots +t_n}\right)}$

Where:

$T_K$ is the mean kinetic temperature in kelvins

$\mathrm{\Delta }H$ is the activation energy (in kJ mol⁻¹)

$R$ is the gas constant (in J mol⁻¹ K⁻¹)

$T_1$ to $T_n$ are the temperatures at each of the sample points in kelvins

$t_1$ to $t_n$ are time intervals at each of the sample points

When the temperature readings are taken at the same interval (i.e., $t_1$ = $t_2$ = $\cdots$ = $t_n$), the above equation is reduced to:

$T_K=\frac{\frac{\mathrm{\Delta }H}{R}}{-\ln \left(\frac{e^{\left(\frac{-\mathrm{\Delta }H}{R{T}_1}\right)}+e^{\left(\frac{-\mathrm{\Delta }H}{R{T}_2}\right)}+\cdots +e^{\left(\frac{-\mathrm{\Delta }H}{R{T}_n}\right)}}{n}\right)}$

Where:

$n$ is the number of temperature sample points