Vapor is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel

Options

A. (a)increases continuously
B. (b)decreases continuously
C. (c)first increases and then decreases
D. (d)first increases and then becomes constant.

Answer

To solve the problem of how the pressure in a closed vessel changes when vapor is injected at a uniform rate, we can break down the solution into clear steps:

### Step-by-Step Solution:

1. **Initial Condition**:
- The vessel is initially evacuated, meaning it contains no gas molecules.
- Therefore, the initial pressure (P_initial) in the vessel is 0 atm.

**Hint**: Remember that pressure is a measure of the force exerted by gas molecules colliding with the walls of the container. If there are no molecules, there is no pressure.

2. **Injection of Vapor**:
- Vapor is injected into the vessel at a uniform rate. This means that the number of gas molecules in the vessel is increasing steadily over time.
- As the number of molecules increases, the pressure in the vessel will also increase according to the ideal gas law (PV = nRT), where n (number of moles) is increasing.

**Hint**: Think about how adding more molecules to a fixed volume increases the frequency of collisions with the walls, thus increasing pressure.

3. **Pressure Increase**:
- Initially, as more vapor is injected, the pressure will rise continuously because the number of molecules is increasing.
- This pressure increase will continue until the pressure reaches the saturated vapor pressure (P_saturated), which is the maximum pressure exerted by the vapor at a given temperature.

**Hint**: Saturated vapor pressure is a key concept; it represents the point where the vapor is in equilibrium with its liquid phase.

4. **Equilibrium Condition**:
- Once the pressure in the vessel equals the saturated vapor pressure, the system reaches a state of equilibrium.
- At this point, any additional vapor injected will not increase the pressure further; instead, it will start to condense back into liquid form.

**Hint**: Understand that at saturation, the rate of vaporization equals the rate of condensation, leading to a constant pressure.

5. **Final Pressure Behavior**:
- After reaching the saturated vapor pressure, the pressure remains constant despite further injection of vapor.
- Thus, the overall behavior of the pressure in the vessel can be described as initially increasing and then becoming constant.

**Hint**: Visualize this behavior as a graph where the pressure rises sharply and then levels off at the saturated vapor pressure.

### Conclusion:
The pressure in the closed vessel first increases as vapor is injected and then becomes constant once the saturated vapor pressure is reached.

### Final Answer:
The correct option is that the pressure first increases and then becomes constant.

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