Container with movable piston at top and valve near bottom is filled an ideal gas. Valve is opened and some gas slowly escapes. Valve is then closed and the piston appears to be at a lower position. System is in thermal equilibrium. Is final pressure of container, greater, less or equal?

Equal: If you find the sum of the forces, you will find that the final pressure and initial pressure are equal because the weight of the piston and the atmospheric pressure remain the same throughout the stages.

To determine whether the final pressure of the container is greater, less, or equal to the initial pressure, we need to consider the changes that occurred in the system.

Initially, the container is filled with an ideal gas, and there is a movable piston at the top, and a valve near the bottom. When the valve is opened, some gas slowly escapes until the valve is closed again. Afterward, the piston appears to be at a lower position.

Here's how we can break down the analysis to determine the final pressure:

1. Movement of the piston: The fact that the piston appears to be at a lower position indicates that the volume of the gas has increased. This expansion suggests that the work is done by the gas during the process because the piston moves upward against gravity. Consequently, the gas has lost some internal energy, resulting in a decrease in the temperature of the gas.

2. Valve closure: When the valve is closed, no more gas can escape from the container, meaning no further changes in volume or number of gas molecules occur.

3. Thermal equilibrium: The system is said to be in thermal equilibrium, which implies that the final temperature of the gas is equal to the initial temperature. This equilibrium results from the system coming to rest and reaching a steady state.

Based on this analysis, we can conclude that the final pressure of the container will be less than the initial pressure. The decrease in volume due to the movement of the piston caused the gas to expand, resulting in a reduction in temperature. According to the ideal gas law (PV = nRT), if the temperature decreases while the volume remains constant, the pressure must also decrease. Hence, the final pressure will be lower than the initial pressure.