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? Do we have to apply the kinetic theory of gases? Do we have to depend on experimental result that the pressure is proportional to temperature?

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Solution

The ideal gas thermometer is based on the ideal gas equation, PV=nRT, where P is pressure of the gas at constant volume V with n number of moles at temperature T. Therefore, P = constant $\times$ T. According to this relation, if the volume of the gas used is constant, the pressure will be directly proportional to the temperature of the gas. We need not use kinetic theory of gases or any experimental results.

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