The Carnot cycle is the theoretical upper bound on heat-engine efficiency: a gas is taken through isothermal expansion (absorbing heat at T_h), adiabatic expansion, isothermal compression (rejecting heat at T_c), and adiabatic compression back to start. Because each step is reversible, no entropy is generated in the ideal case — real engines (real-gas mode) always fall short due to friction and finite-time heat transfer.
η_Carnot = 1 - T_c / T_h
W_cycle = Q_h - Q_c
ΔS_universe ≥ 0 (real engines: > 0)
- Hot reservoir T_h — the heat source temperature; higher T_h raises the theoretical ceiling on efficiency.
- Cold reservoir T_c — the heat sink temperature; a colder sink also raises efficiency.
- Cycle speed — how fast the piston runs through the four strokes; real engines lose efficiency at high speed (not modeled by ideal Carnot).
- Gas model toggle — ideal gas follows the reversible Carnot cycle exactly; real gas adds friction losses, generating entropy and shrinking the P-V loop.
Power-plant turbines and car engines are all judged against the Carnot limit — no real heat engine operating between two fixed temperatures can beat 1 − T_c/T_h.