The temperature in Kelvin is the true thermodynamic temperature. The Kelvin temperature tells you much about the properties of an ideal gas at both at the macrostate level and at the particle level. In thermodynamics, the macrostate refers to the point of view of the quantities you measure in the laboratory such as the pressure, volume and temperature. The particle level is the domain of kinetic theory, where we take the point of view on the particles as having a distribution of velocities. Often we will be using the macrostate to infer the particle level, and vice-versa.
Because for an ideal gas, the temperature on the Kelvin scale is proportional to the product of the pressure and the volume, the Kelvin scale can be obtained via the equation of state for the ideal gas, the ideal gas law. Furthermore, because the internal energy of an ideal gas is proportional to its temperature, we can use the Kelvin temperature to reference internal energy change. If the temperature has increased for an ideal gas, the internal energy has increased.
The Kelvin temperature is also important in the domain of kinetic theory, the part of thermodynamics concerned with the view of the gas particles themselves as a statistical distribution. For a sample of ideal gas, viewed at the particle level, the Kelvin temperature describes the average kinetic energy of the particles.
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