Boyle's Law: pV constant at constant temperature

Steps:

• Initial: pV = k (Boyle's constant).
• Final volume V/2, so final pressure P satisfies P(V/2) = k, thus P = pV/(V/2) = 2p.
• Change Δp = P - p = 2p - p = p.
• Algebraic form: Δp = [pV - p(V/2)] / (V/2) = [pV/2] / (V/2) = p.

Why C is correct:

• Matches Δp = [initial k - initial p × final volume] / final volume, simplifying to p per Boyle's law.

Why the others are wrong:

• A: Adds p instead of subtracting p(V/2), yielding incorrect 2p(V + 1)/V.
• B: Simplifies to p/2, the final pressure if volume doubled, not halved.
• D: Equals 2p, the final pressure, not the change Δp = p.

Final answer: C