How can one check the applicability of the ideal gas equation of state for describing the properties of real gases?

In order to check whether the equation of state of an ideal gas can be used in practice to describe physical processes in gases, an experiment can be performed with atmospheric air enclosed in a corrugated vessel – a bellows. The upper bellows cover is connected to a rod having a screw thread. By rotating this rod, the bellows cover can be raised or lowered, stretching or compressing the bellows and thereby changing its volume.
The scale on the side bar allows you to measure the volume of the bellows in conventional units. To measure the air pressure, the bellows is connected to a pressure gauge. The air temperature can be changed by heating or cooling the bellows.
It follows from the equation of state for an ideal gas that at constant values ​​of the gas mass and molar mass, the ratio of the product of gas pressure and volume to the absolute temperature should have a constant value for any changes in these parameters:
nV / T = mR / M = const