When a liquid is subjected to a 15 atmospheric pressure, then its volume decreases by 0.1%. Then bulk modulus of elasticity (K) of the liquid is (1 atm pressure = `10^(5) N//m^(2)`)

Options

A. `1.5 xx 10^(10) N//m^(2)`
B. `1.4 xx 10^(8) N//m^(2)`
C. `1.5 xx 10^(9) N//m^(2)`
D. `1.4 xx 10^(9) N//m^(2)`

Answer

To find the bulk modulus of elasticity (K) of the liquid when it is subjected to a pressure of 15 atmospheres and its volume decreases by 0.1%, we can follow these steps:

### Step 1: Understand the given data
- The pressure applied (P) = 15 atm
- The volume change (ΔV) = 0.1% of the original volume (V)

### Step 2: Convert the percentage change in volume to a decimal
The change in volume can be expressed as:
\[ \Delta V = 0.1\% \text{ of } V = \frac{0.1}{100} \times V = 0.001V \]

### Step 3: Calculate the volumetric strain
Volumetric strain (ε) is defined as the change in volume (ΔV) divided by the original volume (V):
\[ \epsilon = \frac{\Delta V}{V} = \frac{0.001V}{V} = 0.001 \]

### Step 4: Calculate the change in pressure (ΔP)
The change in pressure (ΔP) is the difference between the final pressure and the initial pressure. Since the initial pressure is atmospheric pressure (1 atm), we have:
\[ \Delta P = P - P_{\text{initial}} = 15 \text{ atm} - 1 \text{ atm} = 14 \text{ atm} \]

### Step 5: Convert ΔP from atmospheres to N/m²
Using the conversion factor \(1 \text{ atm} = 10^5 \text{ N/m}^2\):
\[ \Delta P = 14 \text{ atm} \times 10^5 \text{ N/m}^2/\text{atm} = 1.4 \times 10^6 \text{ N/m}^2 \]

### Step 6: Calculate the bulk modulus (K)
The bulk modulus (K) is defined as the ratio of the change in pressure (ΔP) to the volumetric strain (ε):
\[ K = \frac{\Delta P}{\epsilon} = \frac{1.4 \times 10^6 \text{ N/m}^2}{0.001} = 1.4 \times 10^9 \text{ N/m}^2 \]

### Conclusion
The bulk modulus of elasticity (K) of the liquid is:
\[ K = 1.4 \times 10^9 \text{ N/m}^2 \]