A glass container encloses gas at a pressure `4 xx10^5` Pa and 300 K temperature. The container walls can bear a maximum pressure of `8 xx10^(5)` Pa. If the temperature of container is gradually increased find temperature at which container will break.

Options

A. `600 K`
B. `150 K`
C. `1200 K`
D. `375 K`

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 constant. The relationship can be expressed as:

\[ \frac{P_1}{P_2} = \frac{T_1}{T_2} \]

Where:
- \( P_1 \) = initial pressure of the gas
- \( P_2 \) = maximum pressure the container can withstand
- \( T_1 \) = initial temperature of the gas
- \( T_2 \) = temperature at which the container will break

### Step-by-step Solution:

1. **Identify the Given Values:**
- Initial pressure, \( P_1 = 4 \times 10^5 \) Pa
- Maximum pressure, \( P_2 = 8 \times 10^5 \) Pa
- Initial temperature, \( T_1 = 300 \) K

2. **Set Up the Equation Using Gay-Lussac's Law:**
\[ \frac{P_1}{P_2} = \frac{T_1}{T_2} \]

3. **Substitute the Known Values into the Equation:**
\[ \frac{4 \times 10^5}{8 \times 10^5} = \frac{300}{T_2} \]

4. **Simplify the Left Side:**
\[ \frac{4}{8} = \frac{1}{2} \]
So the equation becomes:
\[ \frac{1}{2} = \frac{300}{T_2} \]

5. **Cross-Multiply to Solve for \( T_2 \):**
\[ 1 \cdot T_2 = 2 \cdot 300 \]
\[ T_2 = 600 \text{ K} \]

6. **Conclusion:**
The temperature at which the container will break is \( T_2 = 600 \) K.

### Final Answer:
The temperature at which the container will break is **600 K**.