A gas of volume 2000ml is kept in a vessel at a pressure of `10^3` pascals at a temperature of `27^@C`. If the pressure is increased to `10^5` pascals at the same temperature, the volume of the gas becomes 

Options

A. 1000ml
B. 20ml
C. 2ml
D. 200ml

Answer

To solve the problem, we will use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. Mathematically, this can be expressed as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial Volume, \( V_1 = 2000 \, \text{ml} \)
- Initial Pressure, \( P_1 = 10^3 \, \text{pascals} \)
- Final Pressure, \( P_2 = 10^5 \, \text{pascals} \)

2. **Write the Boyle's Law Equation:**
\[ P_1 V_1 = P_2 V_2 \]

3. **Rearrange the Equation to Solve for \( V_2 \):**
\[ V_2 = \frac{P_1 V_1}{P_2} \]

4. **Substitute the Known Values into the Equation:**
\[ V_2 = \frac{(10^3 \, \text{pascals}) \times (2000 \, \text{ml})}{10^5 \, \text{pascals}} \]

5. **Calculate the Final Volume \( V_2 \):**
\[ V_2 = \frac{2000000 \, \text{ml}}{10^5} \]
\[ V_2 = \frac{2000000}{100000} \]
\[ V_2 = 20 \, \text{ml} \]

6. **Conclusion:**
The final volume of the gas when the pressure is increased to \( 10^5 \) pascals at the same temperature is \( 20 \, \text{ml} \).

### Final Answer:
The volume of the gas becomes **20 ml**.

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