How this calculator works
Each thermally active quadratic degree of freedom contributes kBT/2 per particle under classical equipartition. Multiply by the number of particles nNA to obtain internal energy f nRT/2. A monatomic gas has three translational degrees; a diatomic gas commonly has two additional rotational degrees near room temperature. The translational energy and mean speed always use the three translational directions. Chemical binding energy and a phase-dependent energy reference are excluded.
Formula
U = (f/2)nRT; mean active-mode energy = (f/2)kBT; mean translational energy = (3/2)kBT; vmean = sqrt(8RT/(pi M)).
Worked example
For 1 mol of monatomic gas at 300 K, U = 3741.508178 J and mean translational energy is 6.2129205e-21 J per particle. With f = 5 at the same conditions, U = 6235.846964 J.
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Frequently asked questions
Are all molecular modes active?
No. Quantum energy spacing can suppress rotation or vibration at low temperature.
Is this sensible heat?
It is a model of internal energy relative to a chosen zero. Heat is energy transferred during a process.
Does increasing f change molecular speed?
At fixed temperature and molar mass, the translational speed distribution is unchanged; extra energy goes into other active modes.