Combined gas law reasoning:\nIf the pressure of a gas is reduced to one-half and its absolute temperature is doubled, how does its volume change (amount of gas fixed)?

Introduction / Context:
Many rapid process estimates in gas handling rely on the combined gas law. Understanding proportional relationships between pressure, temperature, and volume helps in sizing vessels, relief systems, and compressors when moles are constant.

Given Data / Assumptions:

• Ideal-gas approximation holds.
• Amount of gas (n) is constant.
• P2 = 0.5 P1 and T2 = 2 T1; absolute temperatures used.

Concept / Approach:
The combined gas law states: P V / T = constant for a fixed amount of ideal gas. Therefore, V ∝ T/P at constant n. Compute the ratio V2/V1 by applying the given changes in T and P directly to this proportionality.

Step-by-Step Solution:
Write V2/V1 = (T2/P2) / (T1/P1).Substitute T2 = 2T1 and P2 = 0.5P1 → V2/V1 = (2T1/0.5P1) / (T1/P1) = (2/0.5) = 4.Hence, the volume increases by a factor of four.

Verification / Alternative check:
Use PV = nRT: If P halves and T doubles, the right-hand side doubles while the left-hand side has half the pressure; volume must quadruple to balance the equation.

Why Other Options Are Wrong:
One-quarter is the inverse of the correct factor; two times ignores the pressure change magnitude; no change or half-volume contradicts the combined proportionality.

Common Pitfalls:
Forgetting to use absolute temperature; mixing up direct and inverse proportionalities of T and P with V.

Final Answer:
increases four times