The compressibility of water is `4xx10^-5` per unit atmospheric pressure. The decrease in volume of 100 cubic centimetre of water under a pressure of 100 atmosphere will be

Options

A. 0.4 cc
B. `4xx10^-5cc`
C. `0.025cc`
D. `0.004cc`

Explanation

To solve the problem, we need to calculate the decrease in volume of water under a pressure of 100 atmospheres using the given compressibility factor.

### Step-by-Step Solution:

1. **Understand the Formula for Change in Volume**:
The change in volume (\( \Delta V \)) due to pressure can be calculated using the formula:
\[ \Delta V = C \times P \times V \]
where:
- \( C \) is the compressibility,
- \( P \) is the pressure applied,
- \( V \) is the original volume.

2. **Identify the Given Values**:
- Compressibility of water, \( C = 4 \times 10^{-5} \, \text{per atmosphere} \)
- Pressure, \( P = 100 \, \text{atmospheres} \)
- Original volume, \( V = 100 \, \text{cm}^3 \)

3. **Substitute the Values into the Formula**:
Now, substitute the values into the formula:
\[ \Delta V = (4 \times 10^{-5}) \times (100) \times (100) \]

4. **Calculate the Change in Volume**:
- First, calculate \( 100 \times 100 = 10000 \).
- Now, multiply by the compressibility:
\[ \Delta V = 4 \times 10^{-5} \times 10000 \]
- This simplifies to:
\[ \Delta V = 4 \times 10^{-5} \times 10^{4} = 4 \times 10^{-1} \, \text{cm}^3 \]
- Therefore:
\[ \Delta V = 0.4 \, \text{cm}^3 \]

5. **Conclusion**:
The decrease in volume of 100 cubic centimeters of water under a pressure of 100 atmospheres is \( 0.4 \, \text{cm}^3 \).

### Final Answer:
The decrease in volume is \( 0.4 \, \text{cm}^3 \).

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