When the temperature of a gas is `20^(@)C` and pressure is changed from `P_(1)=1.01xx10^(5)Pa` to `P_(2)=1.165xx10^(5)Pa,` then the volume changes by `10%`. The Bulk modulus is

Options

A. `1.55xx10^(5)Pa`
B. `1.01xx10^(5)Pa`
C. `1.4xx10^(5)Pa`
D. `0.115xx10^(5)Pa`

Answer

To find the bulk modulus of the gas, we can follow these steps:

### Step 1: Calculate the change in pressure (ΔP)
The change in pressure (ΔP) can be calculated using the formula:
\[ \Delta P = P_2 - P_1 \]
Where:
- \( P_1 = 1.01 \times 10^5 \, \text{Pa} \)
- \( P_2 = 1.165 \times 10^5 \, \text{Pa} \)

Substituting the values:
\[ \Delta P = 1.165 \times 10^5 - 1.01 \times 10^5 = 0.155 \times 10^5 \, \text{Pa} = 1.55 \times 10^4 \, \text{Pa} \]

### Step 2: Determine the change in volume (ΔV/V)
The volume changes by 10%, which means:
\[ \frac{\Delta V}{V} = \frac{10}{100} = 0.1 \]

### Step 3: Use the bulk modulus formula
The bulk modulus (B) is defined as:
\[ B = \frac{\Delta P}{\frac{\Delta V}{V}} \]

### Step 4: Substitute the values into the bulk modulus formula
Now we can substitute the values we calculated:
\[ B = \frac{1.55 \times 10^4 \, \text{Pa}}{0.1} \]

### Step 5: Calculate the bulk modulus
Calculating the above expression:
\[ B = 1.55 \times 10^4 \, \text{Pa} \times 10 = 1.55 \times 10^5 \, \text{Pa} \]

### Final Answer
The bulk modulus of the gas is:
\[ B = 1.55 \times 10^5 \, \text{Pa} \]

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