A degree of freedom is an independent quadratic coordinate contributing to molecular energy. Every molecule has three translational degrees. A rigid linear molecule has two active rotational degrees; a non-linear molecule has three. Vibrational modes contribute two quadratic terms per mode when thermally active.

Quantum effects can freeze out rotation or vibration at low temperatures, so active f depends on temperature.

A degree of freedom is an independent way a molecule can hold energy in motion. All ideal-gas molecules have three translational directions. A rigid linear diatomic molecule has two relevant rotational axes at ordinary temperatures, giving five active quadratic modes; rotation about its own bond axis contributes negligibly in this simple model. A non-linear rigid molecule may have three rotations. Vibrational modes include both kinetic and potential quadratic terms when active, but may be effectively frozen at low temperature by quantum effects. The active mode count can change with temperature, altering heat capacity. A fixed vector of mean molecular velocity remains zero in a stationary equilibrium sample despite many active modes.

Worked example: For rigid diatomic at room temperature, three translations plus two rotations give f=5.

NCERT trap: Do not automatically count every possible vibration as active at ordinary temperature.

NEET method: Count translations, usable rotations, and only stated active vibrational contributions.

Reading estimate excludes the checks and retake.

Once equipartition applies, f active quadratic terms give total energy U=(f/2)nRT. For a monatomic gas f=3; one mole at 400 K has U≈(3/2)×8.314×400≈5.0 kJ.

Kinetic Theory

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