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Carnot Heat Engine Efficiency Calculator

Nicolas Léonard Sadi Carnot established in 1824 that no heat engine operating between two thermal reservoirs can be more efficient than a reversible Carnot engine.

Temperature of heat source (combustion chamber, steam boiler, nuclear core).

Temperature of ambient cooling sink (cooling tower, river, atmosphere).

Thermal energy input supplied by fuel or steam in kilojoules.

Calculated Result
61.4%

Carnot Thermal Efficiency (η)

Work Produced

614.4 kJ

Heat Rejected

385.6 kJ

Carnot Heat Pump COP

1.63

Carnot Refrigerator COP

0.63

Calculation Breakdown

  1. Absolute Kelvin Thermodynamic TemperaturesT_H = 773.15 K, T_C = 298.15 KTH=TH(°C)+273.15,TC=TC(°C)+273.15T_H = T_H(°C) + 273.15, \quad T_C = T_C(°C) + 273.15
  2. Theoretical Maximum Carnot Efficiency61.44%ηCarnot=1−TCTH\eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H}
  3. Maximum Shaft Work Extracted614.37 kJ (from 1000 kJ input)Wnet=η×QHW_{\text{net}} = \eta \times Q_H
  4. Waste Heat Rejected to Cold Sink385.63 kJQC=QH−WnetQ_C = Q_H - W_{\text{net}}

Carnot Efficiency vs Hot Reservoir Temperature (at T_C = 25°C)

Interactive visualization based on your current inputs

Efficiency (%)
0.019385777100°C250°C500°C750°C1000°CHot Temperature (°C)Carnot Efficiency (%)

What Is the Carnot Heat Engine Efficiency Calculator?

Carnot efficiency represents the absolute maximum theoretical percentage of thermal energy that can be converted into mechanical work by any cyclic heat engine.

It was derived by French military engineer Sadi Carnot in his landmark 1824 treatise on the motive power of fire.

How Does the Carnot Heat Engine Efficiency Calculator Work?

The ideal Carnot cycle consists of four reversible thermodynamic processes: two isothermal expansions/compressions and two isentropic expansions/compressions.

Because total entropy generation for a reversible cycle is zero (ΔS_universe = 0), work output is fundamentally capped by the temperature ratio.

Carnot Heat Engine Efficiency Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

ηCarnot=1−TC,KelvinTH,Kelvin\eta_{\text{Carnot}} = 1 - \frac{T_{C,\text{Kelvin}}}{T_{H,\text{Kelvin}}}

Carnot efficiency is governed strictly by the ratio of absolute Kelvin temperatures. It is impossible to achieve 100% efficiency unless the cold sink is at absolute zero (0 K).

How to Use the Carnot Heat Engine Efficiency Calculator

  1. Enter the hot source temperature and cold sink temperature in Celsius.
  2. Supply the quantity of heat energy input to calculate mechanical work and waste heat.

Step-by-Step Example Calculation

Modern Steam Turbine Thermal Limits

Input Values:

tempHot:500
tempCold:25
heatIn:1000
Worked Steps: Operating between 500°C (773.15 K) and 25°C (298.15 K), maximum theoretical Carnot efficiency is 61.44%, yielding 614.4 kJ of work from 1000 kJ of fuel heat.

Understanding Your Result

Carnot Efficiency (%): Thermodynamic theoretical upper ceiling.

Work Extracted (kJ): Maximum achievable shaft work output.

Rejected Heat (kJ): Minimum waste heat that must be released into the environment.

Factors That Affect the Result

  • Hot Reservoir: Higher peak temperature directly elevates efficiency.
  • Cold Reservoir: Lower cooling temperature improves efficiency.

When Should You Use This Calculator?

  • Power engineering: Evaluating steam turbines, gas turbines, and geothermal systems.
  • Automotive: Benchmarking internal combustion engine thermal performance.

Assumptions & Limitations

  • Assumes a perfectly reversible cycle with zero friction or turbulence.
  • Real engines suffer from finite heat transfer rates and viscous losses.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Fundamental Second Law thermodynamic formulation with 100% theoretical precision.

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