A vessel A has volume V and a vessel B has volume 2V. Both contain some water which has constant volume. The pressure in the space above water is `p_(a)` for vessel A and `p_(b)` for vessel B.

Options

A. (a)`p_(a)=p_(b)`
B. (b)`p_(a)=2p_(b)`
C. (c)`p_(b)=2p_(a)`
D. (d)`p_(b)=4p_(a)`

Answer

To solve the problem, we need to analyze the situation in both vessels A and B, considering the properties of the water and the vapor above it.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- Vessel A has a volume \( V \) and vessel B has a volume \( 2V \).
- Both vessels contain water, which has a constant volume, meaning the amount of water does not change.

2. **Identifying the Pressures**:
- The pressure in the space above the water in vessel A is denoted as \( p_A \).
- The pressure in the space above the water in vessel B is denoted as \( p_B \).

3. **Saturation Condition**:
- Since both vessels contain water, the vapor above the liquid in both vessels will reach a state of saturation.
- In a saturated state, the number of molecules transitioning from the liquid to the vapor phase is equal to the number returning from the vapor to the liquid phase.

4. **Constant Volume Implication**:
- The constant volume of water in both vessels implies that the vapor pressure above the liquid must also be constant.
- This means that the vapor pressure in both vessels must be equal because they are both in a saturated state.

5. **Conclusion**:
- Since both \( p_A \) and \( p_B \) represent the saturated vapor pressure above the water in their respective vessels, we can conclude that:
\[ p_A = p_B \]

### Final Answer:
Thus, the relationship between the pressures in the two vessels is:
\[ p_A = p_B \]