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Physics · Class 11

Compare monatomic and diatomic gases

Kinetic Theory

At constant pressure some heat supplies expansion work, so Cp exceeds Cv by R per mole. More active modes raise both capacities and bring their ratio closer to one.

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Compare monatomic and diatomic gases

நிலையான அழுத்தத்தில் வெப்பத்தின் ஒரு பகுதி விரிவு வேலைக்கு செல்கிறது. ஆகவே மோலார் Cp − Cv = R.

Key notes, relationships and model limits

Key relationship

Cv=fR/2; Cp=Cv+R; γ=(f+2)/f; Q=nCΔT.

Remember

At constant pressure some heat supplies expansion work, so Cp exceeds Cv by R per mole. More active modes raise both capacities and bring their ratio closer to one.

Common trap

Cp and Cv are process-dependent heat requirements, not two different temperatures.

Model limits

Ideal gas with a selected fixed number of active quadratic degrees. Monatomic f=3; rigid diatomic f=5; active vibrational quadratic terms can raise f.

What you will learn

Derive ideal-gas heat capacities from active modes and compare heating constraints.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

For one mole warmed 100 K with f=5, Qv≈2078.62 J and Qp≈2910.06 J; the extra 831.45 J is expansion work.

Why this matters

The model connects compare monatomic and diatomic gases with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

What is γ for a rigid diatomic gas with f=5?

Read the explanation

Cv=5R/2 and Cp=7R/2, so their ratio is 7/5.

Course connection: Class XI Chapter 12. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.