Which of the following relationships correctly expresses the Boyle's law?

Step 1: Analyze the question You are asked which expression correctly states Boyle's law.

Step 2: The concept Boyle's law says that for a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure.

Mathematically:

P ∝ 1/V (at constant T)

or equivalently, PV = constant, so P₁V₁ = P₂V₂.

This means that if you squeeze a gas into half the volume, its pressure doubles.

Step 3: Check each option

• A. P ∝ V at constant T: Wrong. This is direct proportionality, but Boyle's law is an inverse relationship.
• B. V ∝ T at constant P: This is Charles's law, not Boyle's.
• C. P ∝ 1/V at constant T: Correct. Pressure is inversely proportional to volume at constant temperature.
• D. V ∝ 1/T at constant P: Wrong. Volume is directly proportional to T (Charles's law), not inversely.

Step 4: Answer

Tip: Remember the pairs of laws by what is held constant:

• Boyle: constant T, so P and V are inverse (think "B" for "Bounce back": squeeze it and pressure goes up).
• Charles: constant P, so V ∝ T.
• Pressure law (Gay-Lussac): constant V, so P ∝ T.

If the question mentions "constant temperature," the answer almost always involves an inverse relationship between P and V.