A glass vessel is filled up to 3/5th of its volume by mercury. If the volume expansivities of glass and mercury be `9xx 10^(-6)//^(@)C` and `18xx10^(-5)//^(@)C` respectively, then the coefficient of apparent expansion of mercury is

Options

A. `17.1xx10^(-5)//^(@)C`
B. `9.9xx10^(-5)//^(@)C`
C. `17.46xx10^(-5)//^(@)C`
D. `16.5xx10^(-5)//^(@)C`

Explanation

To solve the problem regarding the coefficient of apparent expansion of mercury in a glass vessel, we will follow these steps:

### Step 1: Understand the Concept of Apparent Expansion
The apparent expansion of a liquid when it is contained in a vessel that also expands is given by the formula:
\[ \beta_{apparent} = \beta_{liquid} - \alpha_{vessel} \]
where:
- \(\beta_{apparent}\) is the coefficient of apparent expansion of the liquid,
- \(\beta_{liquid}\) is the coefficient of volume expansion of the liquid (mercury in this case),
- \(\alpha_{vessel}\) is the coefficient of linear expansion of the vessel (glass in this case).

### Step 2: Identify Given Values
From the problem, we have:
- Volume expansivity of mercury, \(\beta_{mercury} = 18 \times 10^{-5} \, \text{°C}^{-1}\)
- Volume expansivity of glass, \(\beta_{glass} = 9 \times 10^{-6} \, \text{°C}^{-1}\)

### Step 3: Calculate the Coefficient of Apparent Expansion
Using the formula for apparent expansion:
\[ \beta_{apparent} = \beta_{mercury} - \beta_{glass} \]
Substituting the known values:
\[ \beta_{apparent} = (18 \times 10^{-5}) - (9 \times 10^{-6}) \]

### Step 4: Perform the Calculation
Calculating the values:
\[ \beta_{apparent} = 18 \times 10^{-5} - 0.9 \times 10^{-5} \]
\[ \beta_{apparent} = 18 \times 10^{-5} - 0.9 \times 10^{-5} = 17.1 \times 10^{-5} \, \text{°C}^{-1} \]

### Step 5: Final Result
Thus, the coefficient of apparent expansion of mercury is:
\[ \beta_{apparent} = 17.1 \times 10^{-5} \, \text{°C}^{-1} \]