Heat engines and efficiency

What a heat engine does

A heat engine is a device that operates in a cycle and converts some heat input into work. It absorbs heat from a high-temperature reservoir, does work on the surroundings, and rejects some heat to a low-temperature reservoir.

Examples include steam turbines, internal combustion engines, gas turbines, and some power plants.

A complete cycle returns the working substance to its initial state. Therefore

$Delta U_{cycle}=0$

By the first law,

$Q_{net}=W_{net}$

for one full cycle.

Energy flow

Let $Q_H$ be heat absorbed from the hot reservoir and $Q_C$ be heat rejected to the cold reservoir, using positive magnitudes. The net work output is

$W=Q_H-Q_C$

The engine cannot convert all $Q_H$ into work. The second law requires some heat rejection for a cyclic engine operating between two reservoirs.

Thermal efficiency

Thermal efficiency is useful work output divided by heat input:

e=rac{W}{Q_H}

Using $W=Q_H-Q_C$,

e=1-rac{Q_C}{Q_H}

Efficiency is always less than 1 for a real heat engine. It is often expressed as a percentage.

Why not 100 percent?

The first law alone would allow $Q_C=0$, meaning all heat input becomes work. The second law forbids this for a cyclic heat engine. Some heat must be rejected to a lower-temperature reservoir.

This is the Kelvin-Planck statement of the second law: no device operating in a cycle can convert heat from a single reservoir entirely into work with no other effect.

PV diagrams and work

Heat engines are often represented on pressure-volume diagrams. The net work done by the gas over one cycle is the area enclosed by the cycle:

$W_{cycle}=oint P,dV$

A clockwise cycle on a PV diagram usually represents positive work output by the engine. A counterclockwise cycle represents work input, as in refrigerators or heat pumps.

Working substance

The working substance may be steam, air, fuel-air mixture, refrigerant, or another fluid. It undergoes processes such as compression, heating, expansion, and cooling. The working substance returns to its initial state each cycle, but energy has been transferred from hot reservoir to work and waste heat.

Power

Power is work per time:

P=rac{W}{Delta t}

An engine's efficiency tells what fraction of heat input becomes work. Its power tells how quickly it produces work. A highly efficient engine may have low power if it operates slowly.

Real losses

Real engines are less efficient than ideal limits because of friction, turbulence, heat transfer across finite temperature differences, incomplete combustion, electrical resistance, and other irreversibilities. These processes produce entropy and reduce useful work output.

The big idea

A heat engine is a cyclic device that converts part of heat input into work while rejecting waste heat. Efficiency is limited by the second law, not merely by engineering imperfections. Real engines can be improved, but no cyclic engine can turn all absorbed heat into work.