Give the kinetic interpretation of temperature.

Explanation

Consider one mole of a gas.
P - pressure, V - volume, T - temperature,
M - molecular mass of the gas, density `rho`.
Accumulate to kinetic theory, the pressure excited by the gas is
`V=(1)/(3)rhoc^(2),P=(1)/(3)(M)/(V).c^(2)" (or) "PV=(1)/(3)Mc^(2)." "...(1)`
`PV=(2)/(3).(1)/(2).Mc^(2)`
`(1)/(2)Mc^(2)` is the average kinetic energy (E) of one mole of the gas.
`therefore PV=(2)/(3).E`
The ideal gas equation for one mole of a gas is
`PV=RT therefore RT=(2)/(3)E" (or) "E=(3)/(2).RT`
The above equation gives the mean K.E of one mole of gas.
`therefore` The mean Kinetic Energy per molecule is proportional to the absolute temperature of the gas.