Why Can a Machine Never Turn All Its Heat Into Work? A Limit Nobody Can Engineer Around

Extracting work from heat requires a flow, and a flow requires a difference. The device takes heat from something hot, converts part of it into work, and rejects the remainder into something colder, which is not a design flaw but a requirement, since without somewhere cooler to reject heat to, nothing flows and no work is produced. Every steam turbine, petrol engine, jet engine and gas turbine follows this pattern, and each needs a cold side as much as a hot one. Power stations are built beside rivers and coasts, and fitted with cooling towers, precisely to supply that cold side, which is why the waste heat is unavoidable rather than a matter of inefficiency.

The maximum possible efficiency depends on the two temperatures and nothing else:

• •Only the hot and cold temperatures matter, not the fuel, the fluid or the design
• •Temperatures must be measured from absolute zero for the relationship to hold
• •Efficiency rises as the hot side gets hotter and the cold side colder
• •A hot side at six hundred degrees and a cold side at twenty caps efficiency near two thirds
• •No real device reaches that ceiling, since it assumes no friction and infinite slowness
• •Real power stations achieve roughly forty to sixty per cent of the heat supplied

The reason is the second law of thermodynamics, which is among the most solidly established statements in physics and which can be put in several equivalent ways. Heat flows from hot to cold on its own and never the other way without work being done. No process can have as its sole result the conversion of heat entirely into work. Disorder in an isolated system does not decrease. Sadi Carnot established the essential result in 1824, before the nature of heat was properly understood, by reasoning about what would happen if a more efficient device existed, and showing that it would permit heat to flow from cold to hot unaided, which contradicts universal experience. The limit is therefore derived from impossibility rather than measured.

The heat that must be rejected is enormous and disposing of it shapes where large machines can be built. A thermal power station rejects more energy as heat than it delivers as electricity, and that heat leaves through cooling towers as evaporating water or into a river, lake or the sea. River cooling raises the water temperature locally, which is regulated because warm water holds less oxygen and changes what can live there, and stations are shut down in heatwaves when the limits would be breached. Cooling towers lose water continuously to evaporation, which is a substantial consumption in dry regions. Some installations use the rejected heat rather than dumping it, supplying district heating networks, greenhouses or industrial processes, which raises the total useful output considerably.

Reversing the arrangement produces a refrigerator or a heat pump, and the same reasoning gives a corresponding limit. Supplying work allows heat to be moved from a cold place to a warmer one, which does not happen unaided, and the amount moved per unit of work supplied is greatest when the two temperatures are close. A heat pump warming a house from outside air at ten degrees moves several units of heat for each unit of electricity used, which is why it beats a direct electric heater by a large factor, and its advantage falls as the outside temperature drops. A refrigerator does the same in the other direction, which is why the back of one is warm and why it heats the room overall.

Converting heat into work requires rejecting part of it somewhere colder, so waste heat is a requirement rather than a design failure, and the maximum efficiency depends only on the two absolute temperatures. Carnot derived the limit in 1824 by showing a better device would let heat flow from cold to hot unaided. Reversing the arrangement moves heat against its natural direction, which is how heat pumps beat direct electric heating.