A one litre flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. The volume of mercury in the flask is `(alpha_(glass)=9xx10^(-6)//^(@)C,gamma_(Hg)=180xx10^(-6)//^(@)C)`

Options

A. `150cm^(3)`
B. `225cm^(3)`
C. `300cm^(3)`
D. `450cm^(3)`

Explanation

To solve the problem, we need to find the volume of mercury in a 1-liter flask, given that the volume of air inside the flask remains constant at different temperatures. We are provided with the coefficients of thermal expansion for glass and mercury.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- The volume of air inside the flask remains constant, which implies that the change in volume of the mercury must equal the change in volume of the glass flask.

2. **Given Data**:
- Volume of the flask (V_flask) = 1 liter = 1000 cm³
- Coefficient of volume expansion for glass (α_glass) = 9 × 10^(-6) /°C
- Coefficient of volume expansion for mercury (γ_Hg) = 180 × 10^(-6) /°C

3. **Volume Change Formulas**:
- Change in volume of glass (ΔV_glass) can be expressed as:
\[ \Delta V_{\text{glass}} = V_{\text{flask}} \cdot 3 \cdot \alpha_{\text{glass}} \cdot \Delta T \]
- Change in volume of mercury (ΔV_mercury) can be expressed as:
\[ \Delta V_{\text{mercury}} = V_{\text{mercury}} \cdot \gamma_{\text{Hg}} \cdot \Delta T \]

4. **Setting Up the Equation**:
- Since the volume of air remains constant, we can equate the two volume changes:
\[ V_{\text{mercury}} \cdot \gamma_{\text{Hg}} \cdot \Delta T = V_{\text{flask}} \cdot 3 \cdot \alpha_{\text{glass}} \cdot \Delta T \]
- The ΔT cancels out from both sides:
\[ V_{\text{mercury}} \cdot \gamma_{\text{Hg}} = V_{\text{flask}} \cdot 3 \cdot \alpha_{\text{glass}} \]

5. **Substituting Values**:
- Substitute the known values into the equation:
\[ V_{\text{mercury}} \cdot (180 \times 10^{-6}) = 1000 \cdot 3 \cdot (9 \times 10^{-6}) \]

6. **Calculating the Right Side**:
- Calculate the right side:
\[ 1000 \cdot 3 \cdot (9 \times 10^{-6}) = 1000 \cdot 27 \times 10^{-6} = 27 \times 10^{-3} = 0.027 \text{ liters} \]

7. **Finding Volume of Mercury**:
- Now, solve for \( V_{\text{mercury}} \):
\[ V_{\text{mercury}} = \frac{0.027}{180 \times 10^{-6}} = \frac{0.027}{0.00018} = 150 \text{ cm}^3 \]

### Final Answer:
The volume of mercury in the flask is **150 cm³**.