A glass bulb is connected to an open-limb manometer. The level of mercury on both limbs was same. The bulb was heated to `57^@C`. If the room temperature and atmospheric pressure are `27^@C` and 750 mmHg, the difference of levels in the two limbs now will be

Options

A. 2.5 cm
B. 5cm
C. 7.5 cm
D. 10 cm

Answer

To solve the problem, we will use the relationship between pressure and temperature given by 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 Given Data**:
- Initial atmospheric pressure (P1) = 750 mmHg
- Initial temperature (T1) = 27°C
- Final temperature (T2) = 57°C

2. **Convert Temperatures to Kelvin**:
- To convert Celsius to Kelvin, use the formula:
\[ K = °C + 273 \]
- For T1:
\[ T1 = 27 + 273 = 300 \, K \]
- For T2:
\[ T2 = 57 + 273 = 330 \, K \]

3. **Use Gay-Lussac's Law**:
- According to Gay-Lussac's law:
\[ \frac{P1}{T1} = \frac{P2}{T2} \]
- Rearranging to find P2:
\[ P2 = P1 \times \frac{T2}{T1} \]

4. **Substitute Values**:
- Substitute the known values into the equation:
\[ P2 = 750 \, mmHg \times \frac{330 \, K}{300 \, K} \]

5. **Calculate P2**:
- Performing the calculation:
\[ P2 = 750 \times 1.1 = 825 \, mmHg \]

6. **Find the Difference in Pressure**:
- The difference in pressure between the two limbs of the manometer is:
\[ \text{Difference} = P2 - P1 = 825 \, mmHg - 750 \, mmHg = 75 \, mmHg \]

7. **Final Answer**:
- The difference in the levels of mercury in the two limbs of the manometer is:
\[ \text{Difference} = 75 \, mmHg \quad \text{or} \quad 7.5 \, cm \]