# How would you determine the volume of a cylinder with fixed volume given air pressure measurements over time and the ability to add more air.

#### Thornack

In the system I am looking at:

We have 3 scuba tanks of constant volumes V1, V2, V3. Any of these fixed volume tanks can be attached to an air compressor but this is done in secret so you do not know which tank was attached. The goal is to determine which of the fixed volume tank has been attached to the compressor. Once attached to the air compressor the fixed volume tank cannot be removed. The air compressor can add more air to the tank by controlling an ON/OFF valve appropriately. You are allowed to monitor the air pressure in the tank and are allowed to determine the change in air pressure over change in time and you know the maximum pressure each tank can withstand is Pmax. You also know that the pressure upstream of the ON/OFF valve equals Pmax before you open the valve.

We also know that Pmax for tank with V1 = Pmax for tank with V2 = Pmax for tank with V3.

is it possible to determine whether the attached tank is V1 or V2 or V3 with the assumption that temperature is fixed?

Is this possible to determine whether the attached tank is V1 or V2 or V3 with the assumption that the temperature increases as you add air?

How would you do this? I am aware of the ideal gas law which describes the relationship between pressure (P) and Volume (V) which is PV=nRT but am unsure where to start. I know that graphing 1/P vs Volume yields a linear graph.