Question

how does the kinetic energy of particles relate to the temperature of the substance containing those particles, also show the equation that relates kinetic energy and temperature.

Answer 1

The speed of molecules in an "ideal" gas is related to the temperature

Advanced work indicates that

1/2 m v^2 = 3/2 k T where v^2 here is the mean square speed

This is true for H2, He, O2, Hg etc. and m is the molecular mass and k the Boltzmann constant