Question

An Underwater Gas Piston. You and your team have been given the task of preparing a gas piston device that is to be deployed to the bottom of the Southern Sea, beneath the Brunt Ice Shelf off the coast of Antarctica. The inner volume of the cylinder has a diameter of 9.40 cm and a length of 24.0 cm, and is fitted with a movable piston that compresses the Argon (Ar) gas that it contains. Before deployment, the piston is located and held at the very top of the cylinder, providing the maximum volume for the gas. When the device is submerged, however, the piston will move inward due to the water pressure due to the depth, and the change in temperature of the gas. The device is to be taken to a depth of 340 m in salt water (density rho = 1.03 g/cm3) at a temperature of 33.0 °F.

If the maximum allowable compression distance of the piston is 14.5 cm, what is the minimum gas pressure that must be attained when the device is filled at the surface (at atmospheric pressure and T = 59.0 °F) in order that the maximum displacement of the piston does not exceed its maximum (14.5 cm) when submerged to a depth of 340 m?

Answer 1

To calculate the minimum gas pressure, use the change in volume and pressure equations.

Step-by-step explanation:

To calculate the minimum gas pressure that must be attained when the device is filled at the surface, we need to consider the change in volume and the change in pressure due to the depth and temperature conditions. The change in volume can be found using the equation V1/V2 = P2/P1, where V1 and V2 are the initial and final volumes, and P1 and P2 are the initial and final pressures. The change in pressure can be found using the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

In this case, we are given the initial volume and temperature of the gas, as well as the maximum displacement of the piston when submerged to a depth of 340 m. We can use these values to calculate the final volume and pressure. The minimum gas pressure needed to ensure that the maximum displacement of the piston does not exceed 14.5 cm can then be calculated based on the final volume and pressure.