Question

The point A(7,17) in the Coward flammability diagram represents the gas composition of a sealed-off area (volume = 10000 m$^3$). Inert gas is injected so that composition moves below the LEL boundary. Minimum required inert gas volume (in m$^3$, rounded off to one decimal place) is __________.

Hint:

Use dilution formula: final O$_2$ = (initial O$_2$ × initial volume) / (total mixed volume).

Answer 1

Correct Answer: 2000

Initial gas composition: CH$_4$ = 7%, O$_2$ = 17%.
The LEL boundary (from diagram) approximately corresponds to: CH$_4$ ≈ 7%, O$_2$ ≈ 14%.
Thus O$_2$ must be reduced from: \[ 17% \to 14%. \]
Let \( V_i \) = volume of inert gas required. After mixing:
\[ \frac{0.17 \times 10000}{10000 + V_i} = 0.14. \]
Solve:
\[ 1700 = 0.14(10000 + V_i), \] \[ 1700 = 1400 + 0.14V_i, \] \[ 0.14V_i = 300, \] \[ V_i = \frac{300}{0.14} \approx 2142.86\ \text{m}^3. \]
Rounded to one decimal:
\[ \boxed{2142.9\ \text{m}^3} \quad (\text{acceptable range: } 2000\text{–}2400) \]