The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is

Options

A. `(1)/(7)`
B. `(7)/(6)`
C. `(6)/(7)`
D. `(1)/(6)`

Answer

To solve the problem, we need to find the ratio of the absolute expansion of the liquid to the apparent expansion of the liquid, given that the absolute coefficient of expansion of the liquid is 7 times that of the volume coefficient of expansion of the vessel.

### Step-by-Step Solution:

1. **Define the Coefficients of Expansion**:
- Let \( \gamma_L \) be the absolute coefficient of expansion of the liquid.
- Let \( \gamma_V \) be the volume coefficient of expansion of the vessel.

2. **Given Relationship**:
- According to the problem, \( \gamma_L = 7 \gamma_V \).

3. **Apparent Coefficient of Expansion**:
- The apparent coefficient of expansion \( \gamma_{\text{apparent}} \) is given by the formula:
\[ \gamma_{\text{apparent}} = \gamma_L - \gamma_V \]

4. **Substituting the Given Values**:
- Substitute \( \gamma_L \) in the equation:
\[ \gamma_{\text{apparent}} = (7 \gamma_V) - \gamma_V = 6 \gamma_V \]

5. **Finding the Ratio**:
- The ratio of the absolute expansion of the liquid to the apparent expansion is given by:
\[ \text{Ratio} = \frac{\gamma_L}{\gamma_{\text{apparent}}} \]
- Substitute the values we found:
\[ \text{Ratio} = \frac{7 \gamma_V}{6 \gamma_V} \]

6. **Simplifying the Ratio**:
- The \( \gamma_V \) cancels out:
\[ \text{Ratio} = \frac{7}{6} \]

### Final Answer:
The ratio of the absolute expansion of the liquid to the apparent expansion of the liquid is \( \frac{7}{6} \).