A flask of volume `10^3` cc is completely filled with mercury at `0^@C` The coefficient of cubical expansion of mercury is `180xx10^(-6)//^(@)C` and heat of glass is `40xx10^(-6)//^(@)C`. If the flask in now placed in boiling water at `100^@C` how much mercury will overflow?

Options

A. 7 cc
B. 14 cc
C. 21 cc
D. 28cc

Explanation

To solve the problem of how much mercury will overflow when a flask filled with mercury is heated from 0°C to 100°C, we can follow these steps:

### Step 1: Calculate the change in volume of the flask
The change in volume of the flask can be calculated using the formula:
\[ \Delta V_{\text{flask}} = \gamma_{\text{flask}} \times V_{\text{flask}} \times \Delta T \]
Where:
- \(\gamma_{\text{flask}} = 40 \times 10^{-6} \, ^\circ C^{-1}\) (coefficient of cubical expansion of glass)
- \(V_{\text{flask}} = 10^3 \, \text{cc}\) (initial volume of the flask)
- \(\Delta T = 100 - 0 = 100 \, ^\circ C\) (change in temperature)

Substituting the values:
\[ \Delta V_{\text{flask}} = 40 \times 10^{-6} \times 10^3 \times 100 = 4 \, \text{cc} \]

### Step 2: Calculate the change in volume of the mercury
The change in volume of the mercury can be calculated using a similar formula:
\[ \Delta V_{\text{mercury}} = \gamma_{\text{mercury}} \times V_{\text{mercury}} \times \Delta T \]
Where:
- \(\gamma_{\text{mercury}} = 180 \times 10^{-6} \, ^\circ C^{-1}\) (coefficient of cubical expansion of mercury)
- \(V_{\text{mercury}} = 10^3 \, \text{cc}\) (initial volume of mercury)
- \(\Delta T = 100 - 0 = 100 \, ^\circ C\)

Substituting the values:
\[ \Delta V_{\text{mercury}} = 180 \times 10^{-6} \times 10^3 \times 100 = 18 \, \text{cc} \]

### Step 3: Calculate the overflow of mercury
To find out how much mercury will overflow, we subtract the change in volume of the flask from the change in volume of the mercury:
\[ \text{Overflow} = \Delta V_{\text{mercury}} - \Delta V_{\text{flask}} \]
Substituting the values:
\[ \text{Overflow} = 18 \, \text{cc} - 4 \, \text{cc} = 14 \, \text{cc} \]

### Final Answer
The amount of mercury that will overflow is **14 cc**.

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