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, it is evacuated, meaning there are no gases present inside. Then, vapor is injected continuously into the vessel. The question asks about the behavior of the pressure of the vapor in the vessel as this process occurs.
Understanding Vapor Behavior in a Closed System
In a closed system, the behavior of gases can be explained using the principles of thermodynamics and the ideal gas law. The ideal gas law states that the pressure (P), volume (V), and temperature (T) of a gas are related by the equation:
PV = nRT
Where:
- P = pressure of the gas
- V = volume of the gas
- n = number of moles of the gas
- R = universal gas constant
- T = absolute temperature
Initial Phase: Injecting Vapor
When vapor is first injected into the evacuated vessel, the number of gas molecules (n) increases while the volume (V) remains constant. Since the temperature (T) is also constant, according to the ideal gas law, the pressure (P) must increase as more vapor is added. This is because more molecules in the same volume will collide with the walls of the vessel more frequently, leading to an increase in pressure.
Equilibrium Phase: Reaching Saturation
As vapor continues to be injected, a point will eventually be reached where the vapor cannot hold any more molecules at that specific temperature. This is known as the saturation point. At this stage, the pressure will stabilize and remain constant. This is because the rate of vapor entering the vessel equals the rate of vapor condensing back into liquid form, maintaining a dynamic equilibrium.
Final Analysis: Answering the Question
Given this understanding, the correct answer to the question is:
b) first increases and then remains constant
Initially, the pressure increases as vapor is injected, and once saturation is reached, the pressure stabilizes. This behavior is typical in closed systems where vapor is involved, and it illustrates the principles of gas behavior under constant temperature conditions.
Real-World Example
Think of a pressure cooker. When you first heat it, steam builds up, and the pressure rises. Eventually, it reaches a point where the steam cannot increase further without condensing back into water, thus maintaining a constant pressure. This analogy helps visualize the concept of vapor pressure in a closed system.
In summary, the pressure of the vapor in the closed vessel will first increase as vapor is injected and then stabilize once saturation is achieved, confirming that option b is the correct choice. If you have any more questions or need further clarification, feel free to ask!
