THERMODYNAMICS · IDEAL CYCLES

Heat engines: Carnot, Otto and Diesel cycles

Compare three ideal thermodynamic cycles of an ideal gas. Explore four processes, net work, heat absorbed and rejected, and thermal efficiency. Time is only an animation parameter.

Version 0.20 beta

Physical parameters

Ready-made examples

Simulation: cylinder and piston

Cylinder and piston use the same geometric scale in both directions; gas colors are symbolic. The cycle is an idealized sequence of equilibrium states.

Animation speed

Time 0 s

Volume V—

Pressure p—

Temperature T—

Cumulative work W (by gas)—

Cumulative heat Q (to gas)—

Internal-energy change ΔU—

Entropy change ΔS—

Current process—

Residual Q − W − ΔU—

Heat absorbed Qᵢₙ—

Heat rejected |Qₒᵤₜ|—

Net cycle work—

Efficiency η—

ΔU = Q − W · Work by the gas positive · Heat into the gas positive

p–V diagram of the cycle / Click a graph to choose a time. Cumulative work starts from state 1 of the cycle.

p–V diagram of the cycle

Pressure versus time

Temperature versus time

First law: Q, W, ΔU

Gas entropy along the cycle

Data table

Assumptions and limitations

Ideal gas of fixed amount and constant heat capacities. Adiabatic legs are reversible and adiabatic; Carnot legs are reversible. Otto and Diesel are air-standard cycles, not real combustion engines. Piston friction, heat leakage, finite-temperature reservoirs, chemical reactions, and actual engine cycle time are not modeled.

THERMODYNAMICS · IDEAL CYCLES

Step-by-step calculations

Calculations use the selected cycle and time; every numeric substitution includes SI units.

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