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:

$T_{K}={\cfrac {\frac {\Delta H}{R}}{-\ln \left({\frac {{t_{1}}e^{\left({\frac {-\Delta H}{RT_{1}}}\right)}+{t_{2}}e^{\left({\frac {-\Delta H}{RT_{2}}}\right)}+\cdots +{t_{n}}e^{\left({\frac {-\Delta H}{RT_{n}}}\right)}}{{t_{1}}+{t_{2}}+\cdots +{t_{n}}}}\right)}}$

Where:

$T_{K}\,\!$ is the mean kinetic temperature in kelvins

$\Delta H\,\!$ 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:

$T_{K}={\cfrac {\frac {\Delta H}{R}}{-\ln \left({\frac {e^{\left({\frac {-\Delta H}{RT_{1}}}\right)}+e^{\left({\frac {-\Delta H}{RT_{2}}}\right)}+\cdots +e^{\left({\frac {-\Delta H}{RT_{n}}}\right)}}{n}}\right)}}$

Where:

$n\,\!$ is the number of temperature sample points