What is thermal efficiency?

Thermal efficiency (η) is the fraction of heat added to a thermodynamic cycle that is converted to net work output. It equals W_net / Q_in, expressed as a percentage. No real engine can exceed the Carnot efficiency for the same temperature limits.

What is Carnot efficiency?

Carnot efficiency is the maximum possible efficiency for any heat engine operating between a hot reservoir at temperature T_hot and a cold reservoir at T_cold (both in Kelvin): η_Carnot = 1 − T_cold / T_hot. It sets a hard upper bound regardless of cycle type.

How is Otto cycle efficiency calculated?

Otto cycle efficiency depends only on the compression ratio r and the specific heat ratio γ (≈1.4 for air): η_Otto = 1 − 1 / r^(γ−1). Higher compression ratios improve efficiency, but real engines are limited by knock.

What is the cutoff ratio in the Diesel cycle?

The cutoff ratio r_c is the ratio of cylinder volume at the end of constant-pressure heat addition to volume at the start (i.e., how far the piston travels while heat is added). A lower cutoff ratio gives higher efficiency. η_Diesel = 1 − [r_c^γ − 1] / [γ · (r_c − 1) · r^(γ−1)].

How does Brayton cycle efficiency work?

The ideal Brayton cycle efficiency depends on the pressure ratio r_p and specific heat ratio γ: η_Brayton = 1 − 1 / r_p^((γ−1)/γ). This applies to ideal gas turbines and jet engines with isentropic compression and expansion.

Why does actual efficiency differ from cycle efficiency?

Real engines lose energy to friction, heat transfer through walls, incomplete combustion, and pressure drop through valves. Actual efficiency is always lower than the ideal cycle efficiency and far below the Carnot limit.

Thermal Efficiency of Heat Engine

Name: Thermal Efficiency of Heat Engine
Availability: InStock
Author: Nham Vu

Compute thermal efficiency for Carnot, Otto, Diesel, and Brayton cycles, or enter measured work output and heat input for actual efficiency.

Cycle Parameters

Cycle Type

Hot Reservoir Temperature

Cold Reservoir Temperature

Select a cycle and enter parameters to compute thermal efficiency.

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Summary

Compute thermal efficiency for Carnot, Otto, Diesel, and Brayton cycles, or enter measured work output and heat input for actual efficiency.

How it works

Select a cycle type: Carnot, Otto, Diesel, Brayton, or Actual.
Enter the required parameters for the selected cycle (temperatures, compression ratio, cutoff ratio, or energy values).
Click Calculate to compute thermal efficiency and see a breakdown of key values.
The Carnot result also shows the efficiency gap between your cycle and the ideal limit.
Use the Copy Result button to copy all values to the clipboard.

Use cases

Evaluate the theoretical upper limit of efficiency for a given heat source and sink.
Estimate Otto cycle efficiency from an engine compression ratio.
Compute Diesel cycle efficiency when you know the compression and cutoff ratios.
Analyze Brayton cycle efficiency for gas turbines using pressure ratio and specific heat ratio.
Calculate actual thermal efficiency from dynamometer work output and fuel heat input.
Compare cycle efficiencies side-by-side to assess design trade-offs.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu