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

Options

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

Explanation

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

### Step 1: Identify the given values
- Initial pressure, \( P_1 = 1.01 \times 10^5 \, \text{Pa} \)
- Final pressure, \( P_2 = 1.165 \times 10^5 \, \text{Pa} \)
- Percentage change in volume, \( \Delta V/V = 10\% = 0.1 \)

### Step 2: Calculate the change in pressure (\( \Delta P \))
The change in pressure can be calculated using the formula:
\[ \Delta P = P_2 - P_1 \]
Substituting the values:
\[ \Delta P = 1.165 \times 10^5 \, \text{Pa} - 1.01 \times 10^5 \, \text{Pa} \]
Calculating this gives:
\[ \Delta P = 0.155 \times 10^5 \, \text{Pa} = 1.55 \times 10^4 \, \text{Pa} \]

### Step 3: Calculate the bulk modulus (B)
The bulk modulus \( B \) is defined as:
\[ B = \frac{\Delta P}{\Delta V/V} \]
Substituting the values we have:
\[ B = \frac{1.55 \times 10^4 \, \text{Pa}}{0.1} \]
Calculating this gives:
\[ B = 1.55 \times 10^5 \, \text{Pa} \]

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

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