Gas cooled at constant pressure (qualitative behavior): When a gas is cooled at constant pressure, what happens to its temperature and volume?

Introduction / Context:Many real processes approximate constant-pressure behavior, such as heating or cooling in ducts and atmospheric processes. Understanding the qualitative change in volume with temperature at constant pressure is a direct application of the ideal gas law and is vital for interpreting P–V–T diagrams and process narratives.

Given Data / Assumptions:

• Ideal gas behavior for qualitative trends.
• Pressure p held constant externally.
• No phase change within the temperature range considered.

Concept / Approach:The ideal gas equation pV = mRT shows V ∝ T at fixed p and mass. Therefore, reducing T (cooling) directly reduces V at constant p. Temperature obviously decreases by definition of cooling. Thus, both the temperature and the volume decrease during constant-pressure cooling.

Step-by-Step Solution:

Verification / Alternative check:On a T–V diagram at constant p, the process traces a straight line through the origin (for ideal gas), confirming direct proportionality between V and T.

Why Other Options Are Wrong:

• Temperature increases while cooling: Contradiction in terms.
• Volume increases under cooling at constant p: Opposite of ideal gas relation.
• Both increase: Again contradicts cooling definition and gas law.

Common Pitfalls:Confusing constant-pressure with constant-volume or constant-temperature processes; forgetting to hold mass constant when applying pV = mRT.

Final Answer:both temperature and volume decreases