Heat Engines and the Second Law
An engine takes heat from a hot reservoir, does work and dumps the rest cold, and no arrangement of parts can skip the dumping. The second law states that limit in terms of what cannot be built.
What a learner can do afterwards
- Computes the efficiency of an engine from the heat taken in and rejected
- States the engine and refrigerator forms of the second law and shows they say the same thing
- Explains why a device converting heat entirely into work is impossible
1 · Read
An engine takes heat Qh from a hot store, turns part into work W, and dumps the rest Qc to a cold store. Efficiency is W over Qh, which equals one minus Qc over Qh. The dumping is not bad design: car engines all need cooling because no arrangement of parts can skip it.
An engine with efficiency 0.60 does 300 J per cycle. The heat drawn is 300 over 0.60, which is 500 J, and the heat dumped is 500 minus 300, which is 200 J. Even this idealised engine throws away 200 J every cycle.
The second law states the limit two ways. Engine form: no cycle can turn heat from one store fully into work. Refrigerator form: heat cannot crawl from cold to hot without work put in. The two say the same thing: a cheat device for one form could drive a cheat device for the other.
Measure temperatures in kelvin before any ratio. Efficiency always lands below one, and any claim above one breaks the law. A refrigerator is not a reversed cheat: its performance still costs work.
Work is heat in minus heat out, efficiency stays below one, and both forms of the second law ban the same cheats.
The rewritten readings were written for this dataset.
More to read
The highest possible engine efficiency
Between fixed hot and cold reservoirs, a Carnot engine reaches the maximum possible efficiency. Its reversible cycle combines two isothermal processes with two adiabatic ones. Efficiency equals 1 minus cold temperature divided by hot temperature, both measured in kelvin.
No engine using those reservoirs can exceed this bound. It is a theoretical limit, not a construction plan. Friction and irreversible heat transfer lower real efficiency. Compare a proposed efficiency with the limit. Increasing the hot temperature or decreasing the cold temperature raises that limit.
Why engines must release heat
Two equivalent statements express the second law. A cyclic engine cannot take heat from a single reservoir and convert all of it into work with no other effect. Heat cannot move from cold to hot without another effect, such as work input. Violating either statement would violate the other.
An engine must release some heat, leaving efficiency below 1. Calculate efficiency by dividing useful work output by heat input, or by subtracting the rejected-heat/input-heat ratio from 1.
Temperature sets the performance limit
For an engine operating between two reservoirs, the Carnot bound depends on their absolute temperatures. Neither the working substance nor the machine's design changes that limit. Steam, petrol and jet engines all obey the second law.
For a refrigerator between two reservoirs, those temperatures also determine the greatest possible coefficient of performance. A claimed performance above the appropriate bound is incompatible with the second law, so check the temperatures and calculated limit before accepting the claim.
Check an engine's entropy balance
For a small reversible heat transfer, entropy changes by the transferred heat divided by absolute temperature. An isolated system's total entropy cannot fall.
A cyclic engine releases entropy with rejected heat. This macroscopic entropy balance explains the requirement for heat rejection and agrees with efficiency limits. If the combined engine and surroundings form an isolated system, a predicted fall in their total entropy rules out the proposed operation. Check this balance when assessing a design.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.