Entropy Generation: An Energy Balance Can Close while a Process Remains Irreversible

Define the Material or Thermodynamic Model

MIT’s entropy discussion distinguishes conserved energy from entropy generation in real irreversible processes. For heat transferred between two fixed-temperature reservoirs without external work, the combined entropy change is Q(1/Tcold − 1/Thot).

Review a Hypothetical Comparison

Assign 100 J of heat moving from 400 K to 300 K. The hot reservoir changes by −0.25 J/K and the cold by +0.33333 J/K, giving +0.08333 J/K in total. Reversing the same passive transfer preserves the 100 J energy account but gives −0.08333 J/K. That sign rejects the reversed passive model; work or another interaction would be required to change its boundary.

Keep the Evidence with the Decision

Write all reservoirs and interactions before summing entropy terms. Keep absolute temperatures and signed heat contributions visible. Use energy closure and entropy generation as complementary model checks.

The reservoirs are invented and held at fixed temperatures. A real finite body, flowing stream or active heat pump needs its corresponding entropy changes; the two-reservoir expression cannot replace that fuller account.

What entropy inventory identifies irreversibility beyond conservation of total energy?

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Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• MIT’s entropy discussion
• Reference from hmpharmamachines.com