A heat engine operates cyclically, absorbing thermal energy from a hot reservoir, converting some of it into useful work, and transferring the remainder to a cold reservoir. Its efficiency is the useful work output divided by the energy absorbed from the hot reservoir.
How a Heat Engine Works
A working substance, usually a gas, undergoes a thermodynamic cycle. During one complete cycle, it returns to its initial state, so its change in internal energy is zero: .
Using the IB sign convention for the first law, , where is work done by the system. Over a complete cycle, the net thermal energy supplied therefore equals the net work done.
On a pressure-volume diagram, the gas expands during part of the cycle and does work on the surroundings. It is compressed during another part, so the surroundings do work on it. The enclosed area represents the net work per cycle; a clockwise cycle gives positive net work by the gas.
| Energy transfer | Meaning |
|---|---|
| Energy absorbed from the hot reservoir | |
| Useful work done by the engine | |
| Energy transferred to the cold reservoir |
Conservation of energy gives:
Therefore, . A heat engine cannot convert all into work because some energy must be transferred to the cold reservoir, in accordance with the .
Calculating Efficiency
The efficiency is
For example, if an engine absorbs and transfers to the cold reservoir:
For an ideal reversible engine, the maximum possible efficiency is the Carnot efficiency:
where both temperatures must be in kelvin.
Exam Technique
This is IB Physics HL-only content from B.4 Thermodynamics. In a calculation, identify , , and , show energy conservation, and express efficiency as either a decimal or percentage. For graph questions, determine net work from the area enclosed by the cycle. A common misconception is that efficiency can reach 100%; for finite reservoir temperatures, it cannot.