A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

Options

A. same everywhere
B. lower in the front side
C. lower in the rear side
D. lower in the upper side

Explanation

To solve the problem, we need to analyze the situation of a closed compartment containing gas that is accelerating in a horizontal direction. We will use the principles of fluid mechanics and thermodynamics to understand how the pressure behaves in this scenario.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a closed compartment filled with gas.
- The compartment is accelerating horizontally with some acceleration \( a \).
- We are neglecting the effect of gravity.

2. **Applying the Concept of Pressure in Accelerating Systems**:
- In a non-inertial frame (the frame of the accelerating compartment), an effective force acts on the gas due to the acceleration. This can be thought of as a pseudo-force acting in the opposite direction of the acceleration.

3. **Pressure Gradient**:
- The pressure in the gas will vary with position due to this pseudo-force. Specifically, the pressure will be higher on the side of the compartment opposite to the direction of acceleration and lower on the side in the direction of acceleration.
- Mathematically, the change in pressure \( \Delta P \) can be described by the equation:
\[ \Delta P = -\rho a \Delta x \]
where \( \rho \) is the density of the gas, \( a \) is the acceleration, and \( \Delta x \) is the distance in the direction of acceleration.

4. **Conclusion about Pressure**:
- Since the pressure decreases in the direction of acceleration, we can conclude that the pressure is not uniform throughout the compartment. Instead, it is higher on the side opposite to the direction of acceleration and lower on the side in the direction of acceleration.

5. **Final Answer**:
- Therefore, the pressure in the compartment is lower in the direction of acceleration and higher on the opposite side.