A gas cylinder containing cooking gas can withstand a pressure of `14.9 atm`. The pressure gauge of cylinder indicates `12 atm` at `27^(@) C`. Due to sudden fire in building the temperature starts rising. The temperature at which the cylinder will explode is

Options

A. `87.5^(@)C`
B. `99.5^(@)C`
C. `115.5^(@)C`
D. `135.5^(@)C`

Explanation

To solve the problem, we will use Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Maximum pressure the cylinder can withstand (P2): 14.9 atm
- Current pressure indicated by the gauge (P1): 12 atm
- Current temperature (T1): 27°C

2. **Convert the Current Temperature to Kelvin:**
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- For our case:
\[ T1 = 27 + 273.15 = 300.15 \text{ K} \approx 300 \text{ K} \]

3. **Apply Gay-Lussac's Law:**
- According to Gay-Lussac's Law, we have:
\[ \frac{P1}{T1} = \frac{P2}{T2} \]
- Rearranging gives us:
\[ T2 = \frac{P2 \times T1}{P1} \]

4. **Substitute the Known Values:**
- Substitute P1, P2, and T1 into the equation:
\[ T2 = \frac{14.9 \text{ atm} \times 300 \text{ K}}{12 \text{ atm}} \]

5. **Calculate T2:**
- Performing the calculation:
\[ T2 = \frac{4470}{12} = 372.5 \text{ K} \]

6. **Convert T2 Back to Celsius:**
- To convert Kelvin back to Celsius, use the formula:
\[ T(°C) = T(K) - 273.15 \]
- Thus:
\[ T2(°C) = 372.5 - 273.15 = 99.35 \text{ °C} \approx 99.5 \text{ °C} \]

7. **Conclusion:**
- The temperature at which the cylinder will explode is approximately **99.5 °C**.