Thermodynamic Boundaries, Power & Efficiency

Thermodynamics is energy accounting under explicit boundaries. MIT’s undergraduate sequence begins with state, heat, work, the first law, steady-flow energy, entropy, reversibility, and the second law ¹.

For a closed system, a common sign convention gives

where heat \(Q\) enters and work \(W\) leaves. For a steady-flow device, mass carries enthalpy, kinetic energy, and potential energy across the boundary. State your sign convention rather than relying on memory.

Power and the automation duty cycle

Energy is accumulated capacity; power is its rate. A 750 W motor drawing rated power for 20 seconds of each 60-second cycle has a simple average of 250 W, but the drive and thermal design must still tolerate peaks. Include idle, hold, acceleration, regeneration, leaks, warm-up, and auxiliaries.

If an axis delivers 300 W of mechanical power while drawing 420 W electrical, instantaneous drive efficiency is 71%. If the entire cell also draws 200 W for controls and 180 W equivalent compressor input, boundary efficiency for that useful axis work is only \(300/800=37.5\%\). Both numbers can be correct because they answer different questions.

The second law changes the question

The first law says energy is conserved; it does not say every joule can become useful work. Friction and throttling convert organized energy into less available forms. Entropy generation identifies irreversibility. In practice, look for large temperature differences, pressure drops, leakage, braking losses, and repeated acceleration of unnecessary mass.

Rules of thumb

• Never compare efficiencies with different boundaries.
• Separate peak power, average power, and total energy per part.
• Count utilities at their upstream cost: compressed air is not free at the cylinder port.
• A reduced cycle time can raise instantaneous power while lowering energy per good part—or do the opposite. Measure both.

Energy ledger

For one machine cycle, list every energy input and output in joules per cycle. Multiply by cycles per year. Add rejected heat because it may become a cooling load. Mark measured, calculated, and estimated values. The resulting Sankey-style ledger becomes a practical target list for improvement.