When an ideal gas undergoes an isothermal expansion, the pressure of the gas in the enclosure falls. This is due to

Options

A. decrease in the change of momentum per collision
B. decrease in the frequency of collision
C. decrease in both the frequency of collision and the change of momentum per collision
D. decrease in neither the frequency of collision nor the change of momentum per collision

Answer

To solve the question about why the pressure of an ideal gas falls during isothermal expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Isothermal Expansion**:
- Isothermal expansion occurs when a gas expands at a constant temperature. According to the ideal gas law, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

2. **Analyze the Ideal Gas Law**:
- Since the temperature \( T \) is constant and the number of moles \( n \) remains unchanged during the expansion, any increase in volume \( V \) must result in a decrease in pressure \( P \) to maintain the equation's balance. This indicates that \( P \) is inversely proportional to \( V \).

3. **Consider the Effect of Expansion**:
- When the gas expands, the volume increases. For example, if the volume changes from \( V_1 \) to \( V_2 \) (where \( V_2 > V_1 \)), the pressure must decrease from \( P_1 \) to \( P_2 \) (where \( P_2 < P_1 \)).

4. **Collision Dynamics**:
- The pressure of a gas is related to the frequency of collisions between gas molecules and the walls of the container. As the volume increases, the molecules have more space to move around, which generally leads to a decrease in the frequency of collisions with the walls.

5. **Conclusion on Pressure Decrease**:
- Since the number of gas molecules remains constant and they are now occupying a larger volume, the frequency of collisions with the walls decreases. This decrease in collision frequency results in a decrease in pressure.

6. **Select the Correct Option**:
- Among the options provided, the correct reason for the decrease in pressure during isothermal expansion is that there is a decrease in the frequency of collision.

### Final Answer:
The pressure of the gas in the enclosure falls due to a decrease in the frequency of collision.

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