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.^[1]

The mean kinetic temperature can be expressed as:

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

Where:

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

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

${\displaystyle R\,\!}$ is the gas constant (in J mol⁻¹ K⁻¹)

${\displaystyle T_{1}\,\!}$ to ${\displaystyle T_{n}\,\!}$ are the temperatures at each of the sample points in kelvins

${\displaystyle t_{1}\,\!}$ to ${\displaystyle t_{n}\,\!}$ are time intervals at each of the sample points

When the temperature readings are taken at the same interval (i.e., ${\displaystyle t_{1}\,\!}$ = ${\displaystyle t_{2}\,\!}$ = ${\displaystyle \cdots }$ = ${\displaystyle t_{n}\,\!}$), the above equation is reduced to:

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

Where:

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