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. none of these

Explanation

To solve the problem, we need to find the ratio of the absolute expansion of a liquid to its apparent expansion when the absolute coefficient of expansion of the liquid is given as 7 times 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 Relation**:
- According to the problem, \( \gamma_L = 7 \gamma_V \).

3. **Understanding Apparent Expansion**:
- The apparent coefficient of expansion \( \gamma_{\text{apparent}} \) can be defined as:
\[ \gamma_{\text{apparent}} = \gamma_L - \gamma_V \]
- This is because the liquid expands, but the vessel also expands, which reduces the effective expansion observed.

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

5. **Finding the Ratio**:
- We need to find the ratio of the absolute expansion to the apparent expansion:
\[ \text{Ratio} = \frac{\gamma_L}{\gamma_{\text{apparent}}} \]
- Substitute the values we have:
\[ \text{Ratio} = \frac{7 \gamma_V}{6 \gamma_V} \]

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

7. **Conclusion**:
- Therefore, the ratio of the absolute expansion to the apparent expansion of the liquid is \( \frac{7}{6} \).

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