Gas cooled at constant pressure (qualitative behavior): When a gas is cooled at constant pressure, what happens to its temperature and volume?
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Aits temperature increases but volume decreases
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Bits volume increases but temperature decreases
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Cboth temperature and volume increases
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Dboth temperature and volume decreases
Answer
Correct Answer: both temperature and volume decreases
Explanation
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:
Hold p constant: pV = mRT ⇒ V = mR*T/p.Decrease T: T ↓ implies V ↓ proportionally.Hence, both T and V fall when cooling at constant p.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