Two marks on a glass rod `10 cm` apart are found to increase their distance by `0.08 mm` when the rod is heated from `0^@ C "to" 100^@ C`. A flask made of the same glass as that of rod measures a volume of `100 cc at 0^@ C`. The volume it measures at `100^@ C` in (cc) is.

Options

A. `100.24`
B. `100.12`
C. `100.36`
D. `100.48`

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Calculate the Coefficient of Linear Expansion (α)

We know that the change in length (ΔL) is given as 0.08 mm when the temperature changes from 0°C to 100°C. The original length (L) is 10 cm, which is equal to 100 mm.

The formula for the coefficient of linear expansion (α) is given by:

\[ \alpha = \frac{\Delta L}{L \cdot \Delta T} \]

Where:
- ΔL = 0.08 mm = 0.08 × 10^{-3} m
- L = 100 mm = 0.1 m
- ΔT = 100°C - 0°C = 100°C

Substituting the values:

\[ \alpha = \frac{0.08 \times 10^{-3}}{100 \times 100} = \frac{0.08 \times 10^{-3}}{10000} = 8 \times 10^{-6} \, \text{°C}^{-1} \]

### Step 2: Calculate the Coefficient of Volume Expansion (β)

The volumetric coefficient of expansion (β) is approximately three times the linear coefficient of expansion (α):

\[ \beta = 3\alpha = 3 \times 8 \times 10^{-6} = 24 \times 10^{-6} \, \text{°C}^{-1} \]

### Step 3: Calculate the Volume at 100°C

The initial volume (V₀) of the flask at 0°C is given as 100 cc. The formula for the change in volume due to temperature change is:

\[ V = V_0 (1 + \beta \Delta T) \]

Where:
- V₀ = 100 cc
- β = 24 × 10^{-6} °C^{-1}
- ΔT = 100°C - 0°C = 100°C

Substituting the values:

\[ V = 100 \times (1 + 24 \times 10^{-6} \times 100) \]

Calculating the term inside the parentheses:

\[ V = 100 \times (1 + 0.0024) = 100 \times 1.0024 = 100.24 \, \text{cc} \]

### Final Answer

The volume of the flask at 100°C is approximately **100.24 cc**.

---