Engineering & Technology · Thermodynamics & Energy Systems

Entropy, irreversibility and the limits of energy conversion

Two bodies at different temperatures come into thermal contact. The warmer loses energy and the cooler gains the same amount. Energy conservation alone would also permit the reverse transfer. Entropy adds the condition that identifies which overall changes can occur without another effect.

Use Forces & Energy in Simple Systems for force, work, power and boundary accounts; Materials, Properties & Everyday Objects provides property vocabulary. Kelvin, moles, enthalpy and entropy are introduced here. Ratios and graph reading are needed; no calculus is required. Every operating record, diagram and numerical case is constructed. Named physical constants and chemical formulas retain their usual meanings; supplied states are not specifications or operating instructions.

Back to the chapter

After reading, you can

Use entropy generation to distinguish conservation of energy from reversibility.

Entropy is a state property with a balance

Entropy S is a thermodynamic state property measured in J/K; specific entropy s is measured in J/(kg·K). Entropy is not another name for energy, nor simply a count of visible untidiness. A body can lose entropy while its surroundings gain more. The second law applies to the complete account, not a demand that every individual object’s S increase.

For closed matter exchanging heat at fixed boundary temperatures Tb,j, ΔS=Σ(Qj/Tb,j)+Sgen. Each Qj is positive into that system, and Sgen≥0 is entropy generated by irreversibility inside the boundary. If boundary temperature varies, account for the heat in appropriately small portions using their respective absolute temperatures; one arbitrary average need not give the correct transfer.

Separate transfer from generation

Entropy crosses with heat and with flowing matter in an open system. Ideal work transfer carries energy without an entropy-transfer term. Entropy generation arises from processes such as friction, mixing or heat flow through a finite temperature difference. The location of generation in an account depends on where the boundary is drawn.

An isolated composite has no entropy crossing its outside boundary, so its total entropy cannot decrease. A closed system is merely closed to matter: cooling can remove entropy with heat. Reversible is the limiting case in which the system and surroundings could both be restored with no net change elsewhere. Slow motion alone does not eliminate friction or every other irreversibility.

Use the second law as an independent check

A reservoir is an ideal body whose temperature remains effectively constant as heat is exchanged. For such a body, its entropy change from heat Q into it is Q/T. This does not assert that arbitrary irreversible heat transfer through a whole device can always be replaced by one Q/T for that device. Its own entropy balance still needs boundary conditions and generation.

The diagram compares two reservoir changes with their combined account. The negative hot-body change is permissible. The positive combined change records the irreversibility of this direct transfer. Energy has not been destroyed; a future opportunity to obtain work from the temperature difference has been reduced.

Hot reservoir change−2.5 J/K, cold reservoir change+3.333333 J/K, combined change+0.833333 J/K. Energy transfer is1000 J in both directions across the internal connection. Reservoir temperatures stay constant.

Check energy and entropy for the same transfer

In an invented short transfer,1000 J leaves a400 K reservoir and enters a300 K reservoir. Reservoir changes are ΔShot=−1000/400=−2.5 J/K and ΔScold=1000/300≈3.333 J/K. Their sum is 5/6≈0.833 J/K.

With no other exchanges, the combined two-reservoir system is isolated, so this sum is its entropy generation. Reversing only the stated transfer would give−0.833 J/K for the isolated composite and violate the second law. A refrigerator can transfer energy the other way because it introduces work and additional exchanges.

Try the reasoning

Must a cooling closed body have increasing entropy?
Show the answer and reasoning
No. Entropy can leave with heat. The isolated total, including relevant surroundings, must have nonnegative generation.
Does a positive entropy-generation result imply energy disappeared?
Show the answer and reasoning
No. Energy conservation still holds; entropy generation indicates irreversibility and lost work opportunity.
Is every slow process reversible?
Show the answer and reasoning
No. Friction, finite temperature differences and other irreversible effects may remain.

What to carry forward

Balance entropy transfer and generation separately. A negative change for one body can coexist with a positive isolated total.

References

Teaching resources and research supporting this lesson’s explanations and examples.