In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature T. How can we verify whether this is true or not? Are we using the kinetic theory of gases? Are we using the experimental result that the pressure is proportional to temperature?
The ideal gas thermometer is based on the ideal gas law. So, it follows ideal gas equation PV=nRT, where R is a proportionality constant known as the ideal gas constant and P is pressure of the gas at constant volume V with n number of moles at temperature T. Therefore, we can say that, P = constant × T. According to this relation, if for a fixed volume, the pressure is directly proportional to the temperature of the gas. To verify this, there is no need to use kinetic theory of gases or any experimental results.