Boyle’s law check:\nFor a fixed mass of an ideal gas at constant temperature, if the volume becomes three times, what happens to the pressure?

Introduction / Context:
Boyle’s law describes the inverse relationship between pressure and volume for a given amount of ideal gas at constant temperature. This simple proportionality is used constantly in compressor, storage, and pipeline calculations.

Given Data / Assumptions:

• Gas amount n constant; temperature constant (isothermal).
• Initial pressure P and volume V; final volume is 3V.

Concept / Approach:
Boyle’s law: P · V = constant. Therefore, P_final = (P_initial · V_initial) / V_final. With V_final = 3V_initial, pressure must decrease in the same ratio.

Step-by-Step Solution:
Start with P1V1 = P2V2.Set V2 = 3V1 → P2 = P1V1/(3V1) = P1/3.Hence, pressure becomes one-third of its original value.

Verification / Alternative check:
Graphically, the isotherm PV = constant is a rectangular hyperbola; tripling V moves along the curve to one-third P, consistent with the formula.

Why Other Options Are Wrong:
3P, 9P, and 9P^2 contradict the inverse proportionality; “unchanged” ignores Boyle’s law entirely.

Common Pitfalls:
Using Celsius rather than ensuring temperature is constant but in absolute units (not needed for Boyle’s law proportionality); forgetting it is the same mass of gas.

Final Answer:
P/3