Gas laws – precise statement of Boyle’s law Choose the correct form of Boyle’s law for a fixed mass of an ideal gas at constant temperature (isothermal conditions).

Introduction / Context:Boyle’s law is one of the foundational gas laws used to describe the behavior of ideal gases. It underlies isothermal compression/expansion calculations in compressors, syringes, and many laboratory operations.

Given Data / Assumptions:

• Ideal gas behavior assumed.
• Temperature held constant (isothermal process).
• Amount of gas (number of moles) held constant.

Concept / Approach:For an isothermal change of a fixed mass of an ideal gas, pressure is inversely proportional to volume. Mathematically, P ∝ 1/V, which integrates to P * V = constant. Either expression is a correct statement of Boyle’s law; the most explicit engineering form used for calculations is P1V1 = P2V2 when comparing two states at the same temperature and moles.

Step-by-Step Solution:

Verification / Alternative check:From the ideal gas law PV = nRT, holding n and T constant gives PV = constant, confirming Boyle’s law directly.

Why Other Options Are Wrong:

• P ∝ V: Opposite of Boyle’s law.
• P/T = constant: That is Gay-Lussac’s relation for fixed V, not Boyle’s law.
• P ∝ 1/V is conceptually correct, but the most complete engineering statement is the constant-product form selected.

Common Pitfalls:Forgetting the “fixed mass and constant temperature” conditions; mixing Boyle’s law with Charles’ or Gay-Lussac’s laws.

Final Answer:P * V = constant, at constant temperature and fixed mass of gas