1.5 Thermodynamics and Heat Engines

Heat Engines Convert Heat to Work

A heat engine absorbs heat from a hot reservoir, converts part of it into useful work, and expels the remaining heat to a cold reservoir. Over a complete cycle, internal energy returns to its starting value, so by the first law of thermodynamics: Q_net = W_net. Engines operate in cycles, often represented on PV diagrams, where the enclosed area equals the net work done.

Efficiency of Heat Engines

Efficiency (e) measures how well an engine converts heat into work: e = W_net / Q_hot = 1 − (Q_cold / Q_hot). No real engine is 100% efficient because some energy is always expelled as waste heat. The Carnot engine is the theoretical maximum efficiency engine, given by e_Carnot = 1 − (T_cold / T_hot), using absolute (Kelvin) temperatures.

Second Law and Entropy

The second law of thermodynamics states heat naturally flows from hot to cold, and no engine can be perfectly efficient (some heat must always be expelled). This is tied to entropy, a measure of disorder, which tends to increase in natural processes. Refrigerators and heat pumps use work input to move heat backward, from cold to hot, consistent with this law.

Key terms

Heat engine

A device that converts heat input into useful work by operating in a cycle between a hot and cold reservoir.

Efficiency formula

e = W_net / Q_hot = 1 − (Q_cold / Q_hot).

Carnot efficiency

e_Carnot = 1 − (T_cold / T_hot), using absolute (Kelvin) temperatures; represents the maximum possible efficiency.

Second law of thermodynamics

Heat flows naturally from hot to cold, and no engine can be 100% efficient; entropy tends to increase.

PV diagram area (cycle)

The area enclosed by a cyclic process on a PV diagram equals the net work done by the engine.

Try an AP-style question

An engine absorbs 1,000 J from the hot reservoir and exhausts 600 J. What is its efficiency?

1. 40%
2. 60%
3. 100%
4. 167%