If the pressure in a closed vessel is reduced by drawing out some gas, the mean free path of the molecules

Options

A. is increased
B. is decreased
C. remains unchanged
D. increases or decreases according to the nature of the gas

Answer

To solve the question regarding the effect of reducing pressure in a closed vessel on the mean free path of gas molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mean Free Path**:
- The mean free path (λ) is defined as the average distance a molecule travels between successive collisions. It is influenced by the number of molecules present in a given volume.

2. **Effect of Pressure on Molecules**:
- Pressure in a gas is directly related to the number of gas molecules in a given volume. When the pressure is reduced by drawing out some gas, the number of gas molecules in the vessel decreases.

3. **Relationship Between Mean Free Path and Number of Molecules**:
- The mean free path is inversely proportional to the number density (n) of the gas molecules. Mathematically, it can be expressed as:
\[ \lambda \propto \frac{1}{n} \]
- As the number of molecules decreases (due to reduced pressure), the number density (n) also decreases.

4. **Conclusion on Mean Free Path**:
- Since the mean free path is inversely related to the number density, a decrease in the number of molecules (and thus a decrease in pressure) leads to an increase in the mean free path. Therefore, the mean free path increases when the pressure is reduced.

5. **Final Answer**:
- The mean free path of the molecules increases when the pressure in a closed vessel is reduced by drawing out some gas.