The coefficient of real expansion of liquid is `7 xx 10^(-4//0)C`. The co efficient of linear ex/pansion of the vessel is `1 xx 10^(-5)//^(0)C`. The coefficient of apparent expansion of the liquid is

Options

A. `7 xx 10^(-4) // ^(0)C`
B. `6 xx // ^(0)C`
C. `67 xx // ^(0)C`
D. `73 xx // ^(0)C`

Explanation

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

### Step 1: Understand the Definitions
- **Real Expansion (γ_real)**: This is the actual expansion of the liquid when heated.
- **Apparent Expansion (γ_apparent)**: This is the expansion of the liquid as observed, which takes into account the expansion of the container.
- **Coefficient of Linear Expansion of the Vessel (γ_vessel)**: This is the expansion of the vessel per unit length when heated.

### Step 2: Write the Formula for Apparent Expansion
The relationship between the real expansion of the liquid, the apparent expansion, and the expansion of the vessel is given by:
\[ \gamma_{apparent} = \gamma_{real} - \gamma_{vessel} \]

### Step 3: Identify Given Values
From the problem statement:
- Coefficient of real expansion of the liquid, \( \gamma_{real} = 7 \times 10^{-4} \, ^\circ C^{-1} \)
- Coefficient of linear expansion of the vessel, \( \gamma_{vessel} = 1 \times 10^{-5} \, ^\circ C^{-1} \)

### Step 4: Convert Linear Expansion of the Vessel to Volume Expansion
Since the vessel expands in three dimensions, we need to convert the linear expansion to volume expansion:
\[ \gamma_{vessel (volume)} = 3 \times \gamma_{vessel} = 3 \times (1 \times 10^{-5}) = 3 \times 10^{-5} \, ^\circ C^{-1} \]

### Step 5: Substitute Values into the Apparent Expansion Formula
Now we can substitute the values into the formula for apparent expansion:
\[ \gamma_{apparent} = \gamma_{real} - \gamma_{vessel (volume)} \]
\[ \gamma_{apparent} = (7 \times 10^{-4}) - (3 \times 10^{-5}) \]

### Step 6: Perform the Calculation
Convert \( 7 \times 10^{-4} \) to the same power of ten as \( 3 \times 10^{-5} \):
\[ \gamma_{apparent} = (70 \times 10^{-5}) - (3 \times 10^{-5}) = (70 - 3) \times 10^{-5} = 67 \times 10^{-5} \, ^\circ C^{-1} \]

### Step 7: Final Result
Thus, the coefficient of apparent expansion of the liquid is:
\[ \gamma_{apparent} = 67 \times 10^{-5} \, ^\circ C^{-1} \]