To tackle this question, let's break down the scenario step by step. We have a closed vessel that is kept at a constant temperature. Initially, the vessel is evacuated, meaning there is no gas inside. When we start injecting vapor into this vessel, we need to consider how the pressure behaves as we add more vapor.
Understanding Vapor Pressure
In a closed system, the pressure of a vapor is determined by its vapor pressure at a given temperature. Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a specific temperature. As we inject vapor into the evacuated vessel, the pressure will initially rise as more vapor molecules enter the space.
Initial Phase of Vapor Injection
When vapor is first introduced, the pressure will increase continuously. This is because the number of vapor molecules in the vessel is increasing, leading to more collisions with the walls of the vessel, which in turn raises the pressure. This phase continues until the vapor reaches a certain concentration.
Equilibrium State
As we continue to inject vapor, we eventually reach a point where the vapor pressure stabilizes. This happens when the rate of vapor entering the vessel equals the rate of vapor condensing back into the liquid phase (if applicable). At this equilibrium point, the pressure will remain constant despite further injection of vapor. This is because the system can only hold a certain amount of vapor at a given temperature, known as the saturation pressure.
Analyzing the Options
Now, let's analyze the options provided in the question:
- a. increases continuously - This is true initially, but not for the entire process.
- b. first increases and then remains constant - This accurately describes the behavior of the pressure as we inject vapor.
- c. first increases and then decreases - This is incorrect, as the pressure does not decrease once equilibrium is reached.
- d. none of the above - This is also incorrect since option b is valid.
Final Thoughts
Based on this analysis, the correct answer is b. first increases and then remains constant. The pressure in the vessel will rise as vapor is injected until it reaches a stable equilibrium point, where it will remain constant as long as the temperature is maintained and no additional vapor is allowed to escape or condense.
