When a liquid is heated in a glass vessel, its coefficient of apparent expension is `1.03xx10^(-3)//^(@)C.` When the same liquid is heated in a copper vessel, its coefficient of apparent expansion is `1.006xx10^(-3)//^(@)C.` If the coefficient of linear expension of copper is `17xx10^(-6)//^(@)C,` then the coefficient of linear expansion of glass

Options

A. `8.5xx10^(-4)//^(@)C`
B. `9xx10^(-6)//^(@)C`
C. `27xx10^(-6)//^(@)C`
D. `10xx10^(-4)//^(@)C`

Explanation

To find the coefficient of linear expansion of glass, we can use the relationship between the coefficients of apparent expansion of the liquid in different vessels and the coefficients of linear expansion of the materials of the vessels.

### Step-by-step Solution:

1. **Understanding Apparent Expansion**:
The coefficient of apparent expansion of a liquid in a vessel is given by the formula:
\[ \beta = \alpha_L + 3\alpha_V \]
where:
- \(\beta\) is the coefficient of apparent expansion of the liquid,
- \(\alpha_L\) is the coefficient of linear expansion of the liquid,
- \(\alpha_V\) is the coefficient of linear expansion of the vessel.

2. **Setting Up the Equations**:
For the glass vessel:
\[ \beta_{glass} = \alpha_L + 3\alpha_{glass} \]
For the copper vessel:
\[ \beta_{copper} = \alpha_L + 3\alpha_{copper} \]

3. **Substituting Known Values**:
Given:
- \(\beta_{glass} = 1.03 \times 10^{-3} \, /^{\circ}C\)
- \(\beta_{copper} = 1.006 \times 10^{-3} \, /^{\circ}C\)
- \(\alpha_{copper} = 17 \times 10^{-6} \, /^{\circ}C\)

We can write the equations as:
\[ 1.03 \times 10^{-3} = \alpha_L + 3\alpha_{glass} \quad (1) \]
\[ 1.006 \times 10^{-3} = \alpha_L + 3(17 \times 10^{-6}) \quad (2) \]

4. **Calculating from Equation (2)**:
First, simplify equation (2):
\[ 1.006 \times 10^{-3} = \alpha_L + 51 \times 10^{-6} \]
Rearranging gives:
\[ \alpha_L = 1.006 \times 10^{-3} - 51 \times 10^{-6} \]
Converting \(51 \times 10^{-6}\) to the same power of ten:
\[ \alpha_L = 1.006 \times 10^{-3} - 0.000051 = 0.000955 \, /^{\circ}C \]

5. **Substituting \(\alpha_L\) back into Equation (1)**:
Now substitute \(\alpha_L\) into equation (1):
\[ 1.03 \times 10^{-3} = 0.000955 + 3\alpha_{glass} \]
Rearranging gives:
\[ 3\alpha_{glass} = 1.03 \times 10^{-3} - 0.000955 \]
\[ 3\alpha_{glass} = 0.000075 \]
Dividing by 3:
\[ \alpha_{glass} = \frac{0.000075}{3} = 0.000025 \, /^{\circ}C \]
\[ \alpha_{glass} = 25 \times 10^{-6} \, /^{\circ}C \]

### Final Answer:
The coefficient of linear expansion of glass is:
\[ \alpha_{glass} = 25 \times 10^{-6} \, /^{\circ}C \]