Question

Calculate the final pressure required to reduce the volume of a gas to one third, if initial pressure is $1.6 \times 10^5 \text{ Nm}^{-2}$.

• A. $5.4 \times 10^5 \text{ Nm}^{-2}$
• B. $1.6 \times 10^5 \text{ Nm}^{-2}$
• C. $2.11 \times 10^5 \text{ Nm}^{-2}$
• D. $4.8 \times 10^5 \text{ Nm}^{-2}$

Hint:

Boyle's law: $P \propto \frac{1}{V}$

Answer 1

The Correct Option is D

Concept: Boyle's law: \[ P_1 V_1 = P_2 V_2 \]

Step 1: Given relation. \[ V_2 = \frac{V_1}{3} \]

Step 2: Substitute. \[ P_1 V_1 = P_2 \left(\frac{V_1}{3}\right) \]

Step 3: Solve. \[ P_2 = 3P_1 = 3 \times 1.6 \times 10^5 \] \[ P_2 = 4.8 \times 10^5 \text{ Nm}^{-2} \]

Step 4: Conclusion.
Final pressure = $4.8 \times 10^5$ Final Answer: Option (D)