Boyle's Law: Isothermal Gas Expansion

Steps:

• Initial conditions: Volume V1 = 3.0 cm³, pressure P1 = 100 kPa.
• Final conditions: Syringe volume = 12 cm³, total volume V2 = 3.0 cm³ + 12 cm³ = 15 cm³ (air expands from vessel into syringe).
• Apply Boyle's law: P1 V1 = P2 V2 (constant temperature).
• Solve for P2: P2 = (P1 V1) / V2 = (100 kPa × 3.0 cm³) / 15 cm³ = 20 kPa.

Why A is correct:

• Boyle's law (P V = constant at fixed T) gives P2 = 20 kPa as the air expands to total 15 cm³.

Why the others are wrong:

• B: Ignores vessel volume, incorrectly using P2 = 100 kPa × (3/12) = 25 kPa.
• C: Misapplies ratio, e.g., 100 kPa × (12/15) = 80 kPa.
• D: Assumes pressure unchanged, violating Boyle's law.

Final answer: A