Thermodynamics answer page. Browse every topic
Thermodynamics FAQ

The Onsager reciprocal relations state:

Cross-coupling coefficients in non-equilibrium thermodynamics are equal by time-reversal symmetry. Onsager's theorem: L_ij = L_ji — the cross-coupling transport coefficients are symmetric, a consequence of microscopic time-reversal symmetry.

Short Answer

Cross-coupling coefficients in non-equilibrium thermodynamics are equal by time-reversal symmetry is the best answer.

Thermodynamics questions usually test sign conventions, state variables, or what is being held constant. Before calculating, decide whether the system is exchanging heat, doing work, or both.

Onsager's theorem: L_ij = L_ji — the cross-coupling transport coefficients are symmetric, a consequence of microscopic time-reversal symmetry.

Why This Answer Is Correct

This is a Hard-level question in Thermodynamics. The prompt is really testing whether you can connect the concept to its defining physical relationship instead of picking a nearby-but-wrong term.

Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.

Choices At A Glance

  • A. Entropy always increases
  • B. Cross-coupling coefficients in non-equilibrium thermodynamics are equal by time-reversal symmetry
  • C. Heat engines always have efficiency < 1
  • D. Pressure and volume fluctuations are uncorrelated

When similar options appear on an exam, eliminate the ones that break the core law, use the wrong units, or confuse a definition with a consequence.

Topic Snapshot

Topic: Thermodynamics

Difficulty: Hard

Best next move: Re-state the governing law in your own words, then solve one more example from the same topic before moving on.