A sample of gas having volume of 2 m3 is compressed in such a manner so that its pressure is increased by 75 %. The operation is done for a fixed mass of gas at constant temperature. Calculate the final volume of gas

To solve this problem, we can use Boyle's Law, which states that for a fixed mass of gas at constant temperature, the pressure and volume are inversely proportional:

\[
P_1 V_1 = P_2 V_2
\]

Where:
- \( P_1 \) and \( V_1 \) are the initial pressure and volume.
- \( P_2 \) and \( V_2 \) are the final pressure and volume.

### Step 1: Understand the problem

- Initial volume, \( V_1 = 2 \, \text{m}^3 \)
- Initial pressure, \( P_1 \) (we will use \( P_1 \) as a reference, e.g., 1 unit)
- Final pressure, \( P_2 = P_1 + 0.75P_1 = 1.75P_1 \)

### Step 2: Apply Boyle's Law

Using the equation \( P_1 V_1 = P_2 V_2 \):

\[
P_1 \times 2 \, \text{m}^3 = 1.75P_1 \times V_2
\]

Since \( P_1 \) is the same on both sides, it cancels out:

\[
2 \, \text{m}^3 = 1.75 \times V_2
\]

### Step 3: Solve for \( V_2 \)

\[
V_2 = \frac{2 \, \text{m}^3}{1.75} \approx 1.14 \, \text{m}^3
\]

### Final Answer

The final volume of the gas is approximately **1.14 m³**.

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. How would the volume change if the pressure was doubled instead of increased by 75%?
2. What would happen to the volume if the temperature was not constant?
3. How can Boyle's Law be applied to a real-life scenario, such as in a bicycle pump?
4. How do you determine the relationship between pressure, volume, and temperature using the Ideal Gas Law?
5. What assumptions are made when applying Boyle’s Law?

**Tip:** Boyle's Law is only accurate for ideal gases. Real gases can deviate from this behavior, especially at high pressures or low temperatures.

Learn how to calculate the final volume of a sample of gas compressed under constant temperature using Boyle's Law. This problem involves understanding the inverse relationship between pressure and volume, with a step-by-step solution provided.

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