A flask cotaines `100c.c` of a liquid at `10^(@)C`. When it is heated to `110^(0)C` increase in volume of the liquid appers to be 2 c.c. Find the coefficient of real expansion of the liquid.
(`alpha` of flask is `11 xx 10^(-6 //@)C`)

Options

A. `2.33 xx 10^(-4) // ^(@)C`
B. `3.33 xx 10^(-4) // ^(@)C`
C. `23.3 xx 10^(-4) // ^(@)C`
D. `33.3 xx 10^(-4) // ^(0)C`

Explanation

To find the coefficient of real expansion of the liquid, we can follow these steps:

### Step 1: Identify the given values
- Initial volume of liquid, \( V_0 = 100 \, \text{cc} \)
- Initial temperature, \( T_1 = 10^\circ C \)
- Final temperature, \( T_2 = 110^\circ C \)
- Change in volume, \( \Delta V = 2 \, \text{cc} \)
- Coefficient of linear expansion of the flask, \( \alpha_{flask} = 11 \times 10^{-6} \, /^\circ C \)

### Step 2: Calculate the change in temperature
\[ \Delta T = T_2 - T_1 = 110^\circ C - 10^\circ C = 100^\circ C \]

### Step 3: Calculate the coefficient of apparent expansion of the liquid
The formula for the coefficient of apparent expansion (\( \beta \)) is given by:
\[ \beta = \frac{\Delta V}{V_0 \cdot \Delta T} \]
Substituting the known values:
\[ \beta = \frac{2 \, \text{cc}}{100 \, \text{cc} \cdot 100^\circ C} = \frac{2}{10000} = 2 \times 10^{-4} \, /^\circ C \]

### Step 4: Calculate the coefficient of real expansion of the liquid
The relationship between the coefficient of apparent expansion (\( \beta \)), the coefficient of real expansion (\( \gamma \)), and the coefficient of linear expansion of the flask (\( \alpha_{flask} \)) is given by:
\[ \gamma = \beta + \alpha_{flask} \]
Substituting the values we have:
\[ \gamma = 2 \times 10^{-4} + 11 \times 10^{-6} \]
Converting \( 11 \times 10^{-6} \) to the same power of ten:
\[ 11 \times 10^{-6} = 0.11 \times 10^{-4} \]
Now adding:
\[ \gamma = 2 \times 10^{-4} + 0.11 \times 10^{-4} = 2.11 \times 10^{-4} \, /^\circ C \]

### Step 5: Final result
Thus, the coefficient of real expansion of the liquid is:
\[ \gamma = 2.11 \times 10^{-4} \, /^\circ C \]