Thermodynamic Cycle Calculator

Analyze thermodynamic cycles including Carnot, Otto, Diesel, Brayton, and Rankine cycles. Calculate efficiency, work output, and heat transfer.

Carnot Cycle
Otto Cycle
Diesel Cycle
Brayton Cycle
Rankine Cycle
Custom Fluid Properties
kJ/kg·K
kJ/kg·K
kJ/kg·K
Current Fluid Properties

Specific Heat Ratio (γ): 1.4

Specific Heat (cp): 1.005 kJ/kg·K

Specific Heat (cv): 0.718 kJ/kg·K

Gas Constant (R): 0.287 kJ/kg·K

K
K
kg/s

Understanding Thermodynamic Cycles

Thermodynamic cycles are sequences of processes that exchange heat and work with the environment. They are used in engines, refrigerators, and power plants to convert energy from one form to another.

Key Insight: The efficiency of a heat engine is given by η = 1 - QL/QH = Wnet/QH, where QH is heat added, QL is heat rejected, and Wnet is net work output.

Common Thermodynamic Cycles

1

Carnot Cycle: The most efficient possible heat engine cycle. Consists of two isothermal and two adiabatic processes. Serves as an ideal benchmark for real cycles.

2

Otto Cycle: The ideal cycle for spark-ignition internal combustion engines. Consists of isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection.

3

Diesel Cycle: The ideal cycle for compression-ignition engines. Similar to Otto cycle but with constant-pressure heat addition instead of constant-volume.

4

Brayton Cycle: The ideal cycle for gas turbine engines. Consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection.

5

Rankine Cycle: The ideal cycle for steam power plants. Consists of isentropic compression (pumping), constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection.

Cycle Efficiency Formulas

Cycle Efficiency Formula Key Parameters
Carnot η = 1 - TL/TH TH, TL
Otto η = 1 - 1/rγ-1 Compression ratio (r), specific heat ratio (γ)
Diesel η = 1 - (1/rγ-1)[(rcγ-1)/(γ(rc-1))] Compression ratio (r), cut-off ratio (rc), specific heat ratio (γ)
Brayton η = 1 - 1/rp(γ-1)/γ Pressure ratio (rp), specific heat ratio (γ)
Rankine η = (h3 - h4) / (h3 - h2) Enthalpies at different states

Typical Cycle Efficiencies

Cycle Type Typical Efficiency Applications
Carnot (Ideal) 60-70% Theoretical maximum
Otto (Gasoline Engine) 25-30% Automobile engines
Diesel (Diesel Engine) 30-40% Truck, ship engines
Brayton (Gas Turbine) 35-45% Jet engines, power plants
Rankine (Steam Power) 30-40% Power plants
Combined Cycle 50-60% Advanced power plants

Performance Tip: To improve cycle efficiency, increase the temperature difference (TH - TL) for Carnot cycles, increase compression ratio for Otto and Diesel cycles, or increase pressure ratio for Brayton cycles. Material limitations often constrain practical efficiency improvements.

Frequently Asked Questions

The Carnot cycle is the most efficient possible heat engine cycle because it operates between two thermal reservoirs and all processes are reversible. No heat engine operating between the same two temperatures can have a higher efficiency than a Carnot engine. This is a consequence of the second law of thermodynamics.

The main difference is in the heat addition process. The Otto cycle has constant-volume heat addition (spark ignition), while the Diesel cycle has constant-pressure heat addition (compression ignition). Diesel cycles typically have higher compression ratios and can achieve higher efficiencies than Otto cycles, but they operate at higher pressures and temperatures.

Regeneration uses waste heat from the exhaust to preheat the working fluid before it enters the heat addition process. This reduces the amount of external heat needed, thereby increasing efficiency. Regeneration is commonly used in Brayton and Rankine cycles to improve performance.

Real cycle efficiency is limited by several factors including: irreversibilities (friction, heat transfer across finite temperature differences), material temperature limits, component inefficiencies (turbine, compressor, pump), and practical design constraints. Real engines typically achieve 50-80% of their ideal cycle efficiency.

The specific heat ratio (γ = cp/cv) affects how much temperature changes during adiabatic processes. A higher γ value means the gas temperature rises more during compression and drops more during expansion. This affects cycle efficiency - for example, Otto cycle efficiency increases with higher compression ratios, and the effect is more pronounced for gases with higher γ values.