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Physics · Class 11

Distribute energy across active modes

Kinetic Theory

Equipartition assigns equal average energy to each active quadratic degree of freedom. Adding active rotational or vibrational terms raises total energy and heat capacity at the same temperature. A vibrational mode contributes two quadratic terms.

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Distribute energy across active modes

செயல்படும் ஒவ்வொரு இருபடிச் சுதந்திரக் கூறுக்கும் சராசரியாக ½kBT ஆற்றல் கிடைக்கும். கூறுகள் அதிகரித்தால் உள் ஆற்றல் அதிகரிக்கும்.

Key notes, relationships and model limits

Key relationship

Each active quadratic degree contributes ½kBT per molecule; U=f nRT/2.

Remember

Equipartition assigns equal average energy to each active quadratic degree of freedom. Adding active rotational or vibrational terms raises total energy and heat capacity at the same temperature. A vibrational mode contributes two quadratic terms.

Common trap

A vibrational oscillator supplies kinetic and potential quadratic terms.

Model limits

Classical equipartition only for thermally active quadratic modes. Quantum freezing at low temperatures and vibrational activation are represented by choosing f, not by an automatic temperature-dependent mode calculation.

What you will learn

Count active quadratic terms and apply equipartition.

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

At f=5, n=1 mol and T=300 K, each quadratic mode has RT/2≈1247.17 J and the total is 6235.85 J.

Why this matters

The model connects distribute energy across active modes with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

For five active degrees of freedom, what is molar Cv?

Read the explanation

U=5nRT/2, so differentiating with respect to T gives Cv=5R/2 per mole.

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