Charles’s law application at constant pressure:\nA gas at 0°C is cooled at constant pressure until its volume becomes half. What is the final gas temperature?

Introduction / Context:
Charles’s law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: V ∝ T (K). This relation is frequently used for quick estimates of temperature changes when volume changes at constant pressure in ideal-gas approximations.

Given Data / Assumptions:

• Initial temperature T1 = 0°C = 273 K.
• Final volume V2 = 0.5 V1 (half the original).
• Ideal-gas behavior and constant pressure.

Concept / Approach:
From Charles’s law, V1/T1 = V2/T2. Halving the volume halves the absolute temperature. Convert temperatures to Kelvin before applying proportionality to avoid negative values and to maintain linearity of the relation. After computing T2 in Kelvin, convert back to °C for the final answer if needed.

Step-by-Step Solution:

Verification / Alternative check:
Sanity check: Lower volume at constant pressure implies lower temperature; the result should be below 0°C but above absolute zero, which −136.5°C satisfies.

Why Other Options Are Wrong:

• 0°C or 0 K contradict the halving relation; 0 K is unattainable and would imply zero volume.
• −136.5 K is invalid since Kelvin cannot be negative.
• −273°C would imply T = 0 K, not half of 273 K.

Common Pitfalls:
Using Celsius directly in proportionality; forgetting to convert back to °C after computation; proposing negative Kelvin values.

Final Answer:
−136.5°C.