Carnot Engine
η = 1 − T_c/T_h — ideal max efficiency.
Key Notes
Carnot engine: theoretical ideal engine — most efficient possible between two reservoirs at temperatures T_hot and T_cold.
Cycle: isothermal expansion at T_hot → adiabatic expansion → isothermal compression at T_cold → adiabatic compression.
Carnot efficiency: η_Carnot = 1 − T_cold/T_hot (temperatures in KELVIN!).
All reversible engines between same two reservoirs have SAME efficiency = η_Carnot.
No real engine can exceed Carnot efficiency (2nd law of thermodynamics).
Engine output = work; engine sucks heat Q_h from hot, dumps Q_c to cold, produces W = Q_h − Q_c.
Carnot engine is REVERSIBLE — can run backward as a refrigerator with max COP.
Higher T_hot or lower T_cold ⇒ higher efficiency.
Formulas
Carnot efficiency
T in Kelvin. Upper bound for any engine.
Heat-temperature ratio (reversible)
Defines absolute T scale.
Work output
Maximum for given Q_h and reservoirs.
Carnot refrigerator COP
Maximum cooling per unit work; can be > 1.
Important Points
Carnot is THEORETICAL — assumes infinitely slow, reversible processes. Real engines never reach it.
Temperatures MUST be in KELVIN for the formula to work.
η_Carnot = 0 if T_c = T_h (no temperature difference, no engine).
η_Carnot < 1 always — impossible to convert ALL heat to work (Kelvin's statement of 2nd law).
Carnot's theorem: ALL reversible engines between same T have same η. Irreversible engines are LESS efficient.
Real-world: power plants reach 40-50% efficiency vs Carnot limit of ~65% at typical T_h/T_c.
Carnot Engine notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.