The marsh gas detector used by miners works on the principle of

Options

A. Difference in the rates of diffusion of gases
B. Avogadro's hypothesis
C. Gay-Lussac's law of gaseous volumes
D. Berzelius hypothesis

Explanation

To solve the question regarding the principle on which the marsh gas detector used by miners operates, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Marsh Gas**: Marsh gas, primarily composed of methane (CH₄), is a flammable gas that can accumulate in mines and pose serious safety risks to miners.

2. **Principle of Operation**: The marsh gas detector operates on the principle of the difference in the rate of diffusion of gases. This principle is based on Graham's law of effusion and diffusion.

3. **Graham's Law**: According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (molecular weight). Mathematically, this can be expressed as:
\[ \frac{r_1}{r_2} = \sqrt{\frac{m_2}{m_1}} \]
where \( r_1 \) and \( r_2 \) are the rates of diffusion of two gases, and \( m_1 \) and \( m_2 \) are their respective molar masses.

4. **Application in Marsh Gas Detector**: In the context of the marsh gas detector, the device detects methane by comparing its diffusion rate with that of air or other gases present in the mine. Since methane has a lower molecular weight compared to many other gases, it diffuses at a different rate.

5. **Conclusion**: Therefore, the marsh gas detector works by measuring the difference in the rate of diffusion of methane compared to other gases, allowing miners to detect the presence of marsh gas effectively.

### Final Answer:
The marsh gas detector used by miners works on the principle of the difference in the rate of diffusion of gases, which is inversely proportional to their molecular weights.

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