The real coefficient of volume expansion of glycerine is `0.000597per^(@)C` and linear coefficient of expansion of glass is `0.000009par^(@)C` . Then the apparent volume coefficient of glycerine is

Options

A. `0.00058per^(@)C`
B. `0.00057per^(@)C`
C. `0.00027per^(@)C`
D. `0.00066per^(@)C`

Explanation

To find the apparent volume coefficient of glycerine, we can use the relationship between the real coefficient of volume expansion of a liquid and the linear coefficient of expansion of the container (in this case, glass). The formula we will use is:

\[ \text{Apparent Volume Coefficient} (\gamma) = \text{Real Volume Coefficient} - 3 \times \text{Linear Coefficient of Expansion of Glass} (\alpha) \]

### Step-by-step Solution:

1. **Identify the given values**:
- Real coefficient of volume expansion of glycerine (\( \gamma_g \)) = 0.000597 per °C
- Linear coefficient of expansion of glass (\( \alpha_g \)) = 0.000009 per °C

2. **Calculate the term \( 3 \times \alpha_g \)**:
\[ 3 \times \alpha_g = 3 \times 0.000009 = 0.000027 \]

3. **Substitute the values into the formula**:
\[ \text{Apparent Volume Coefficient} (\gamma) = \gamma_g - 3 \times \alpha_g \]
\[ \gamma = 0.000597 - 0.000027 \]

4. **Perform the subtraction**:
\[ \gamma = 0.000570 \]

5. **Convert to scientific notation (if necessary)**:
\[ \gamma = 5.70 \times 10^{-4} \text{ per °C} \]

6. **Final Answer**:
The apparent volume coefficient of glycerine is \( 0.000570 \text{ per °C} \) or \( 5.70 \times 10^{-4} \text{ per °C} \).