By how much will the mean free path of a gas molecule is a vessel at constant `P` change if the temperature is reduced by `20%`?

Options

A. `12.5%` decrease
B. `12.5%` increase
C. `80%` decrease
D. `80%` increase

Explanation

To solve the problem of how the mean free path of a gas molecule changes when the temperature is reduced by 20% at constant pressure, we can follow these steps:

### Step 1: Understand the relationship between mean free path, temperature, and pressure.
The mean free path (λ) of a gas molecule is directly proportional to the temperature (T) and inversely proportional to the pressure (P). Mathematically, this can be expressed as:
\[ \lambda \propto \frac{T}{P} \]

### Step 2: Set up the equation for two different states.
At two different states (initial and final), we can express the relationship as:
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