Question

A spherical tank of 2.0 m diameter is filled with a hazardous liquid of density 1000 kg/m³. The tank is 75% full (by volume) initially, when a leak of 50 mm diameter develops at a point on the surface at the central circumference of the tank. If the vapor space of the tank is pressurized with nitrogen to a constant pressure of 1 atm absolute, what is the time needed for the flow due to the leak to cease?

Answer 1

To calculate the final pressure in a gas cylinder after a temperature change, one can use the ideal gas law. If no gas leaks and there's no phase change, the initial number of moles can be determined and used to find the final pressure after cooling.

Step-by-step explanation:

To solve problems regarding pressure changes in a gas cylinder, such as those involving a leaking high-pressure gas cylinder or changes in conditions like temperature or volume, we typically use the ideal gas law given as PV = nRT. When conditions change, this equation allows us to solve for the unknown, for instance, the final pressure after temperature changes or after a gas leak.

Imagine we have a 50.0 L cylinder of gas at 1.40×107 N/m² and a temperature of 25.0°C. After cooling to -78.5°C, we want to find the final pressure assuming no gas escapes and there is no phase change. We can use the ideal gas law in the following manner:

1. Calculate the number of moles n initially using the initial conditions and the ideal gas law.
2. Apply the ideal gas law again using the final temperature and the calculated n to find the final pressure.

If gas does escape, the number of moles will change, affecting the final pressure. Similarly, we can determine what temperature would be needed to reach a final pressure of 1.00 atm.

Concerning whether cooling the tank is a practical solution, the decision must be based on safety considerations and the efficiency of reducing pressure to a level that allows for safe repairs.