Final answer:
To achieve equilibrium, the air pressure in the blind end of a cylinder must be equal to the atmospheric pressure plus any additional applied pressure. Pascal's principle dictates this, ensuring that P1 = P2 within the fluid.
Step-by-step explanation:
In order to produce equilibrium, the air pressure in the blind end of a cylinder must be equal to the air pressure acting on the other end. According to Pascal's principle, pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and to all walls of the container. This means that if a force is applied on one piston, generating pressure P1, it creates an equal pressure P2 on the other piston, so P1 = P2. Therefore, the air pressure in the blind end must counterbalance the sum of the atmospheric pressure and any additional pressure resulting from forces applied to the piston.
For instance, if the external pressure pushing on the barrel (P1) is the sum of atmospheric pressure (1.0 atm) and the pressure from a 2.2-N force, the pressure in the blind end of the cylinder (P2) must be equal to this combined pressure to maintain equilibrium. This is consistent across different scenarios, including those involving gas-filled balloons, where the inside pressure must match the outside atmospheric pressure for equilibrium unless there is an additional force involved, such as the buoyant force on a hot-air balloon.