Carnot Heat Engine Thermal Efficiency & Heat Pump / Refrigerator COP Calculator

Find theoretical maximum Carnot efficiency, Heat Pump COP, and Chiller COP.

Carnot Maximum Thermal Efficiency
53.85 %
Maximum Mechanical Work Output 269.23 kW
Carnot Heat Pump COP (Heating) 1.86 COP
Carnot Refrigerator COP (Cooling) 0.86 COP
Inputs
K
Hot source absolute temperature (T_H) in Kelvin.
K
Cold sink absolute temperature (T_C) in Kelvin.
kW
Thermal power input (Q_H) in kilowatts.
Results & Graph
Carnot Maximum Thermal Efficiency
53.85 %
Maximum Mechanical Work Output
269.23 kW
Carnot Heat Pump COP (Heating)
1.86 COP
Carnot Refrigerator COP (Cooling)
0.86 COP

Carnot Maximum Thermal Efficiency

Graph 1 • Hot Reservoir Kelvin Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 % 37.4 % 74.8 % 50%: 7.69 % 7.7 50% 75%: 38.46 % 38.5 75% 100%: 53.85 % 53.9 100% 125%: 63.08 % 63.1 125% 150%: 69.23 % 69.2 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Carnot Maximum Thermal Efficiency 53.85 % Maximum Mechanical Work Output 269.23 kW Carnot Heat Pump COP (Heating) 1.86 COP Carnot Refrigerator COP (Cooling) 0.86 COP
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Carnot Maximum Thermal Efficiency53.85 %Maximum Mechanical Work Output269.23 kWCarnot Heat Pump COP (Heating)1.86 COPCarnot Refrigerator COP (Cooling)0.86 COP
Summary: Between T_H=650 K and T_C=300 K, maximum Carnot efficiency is 53.85%, yielding up to 269.23 kW mechanical work from 500 kW heat input.
Summary: Between T_H=650 K and T_C=300 K, maximum Carnot efficiency is 53.85%, yielding up to 269.23 kW mechanical work from 500 kW heat input.
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Formula & Mathematical Methodology: Carnot Efficiency & COP Physics & Engineering Equation

ηCarnot = 1 − (TcoldK / ThotK)
COPheating = ThotK / (ThotK − TcoldK)
η_Carnot = 1 − (T_cold_K / T_hot_K); COP_heating = T_hot_K / (T_hot_K − T_cold_K)
  • hotReservoirKelvin: Hot Reservoir Kelvin (K)
  • coldReservoirKelvin: Cold Reservoir Kelvin (K)
  • heatInputKw: Heat Input Kw (kW)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Carnot Efficiency & COP

Find theoretical maximum Carnot efficiency, Heat Pump COP, and Chiller COP.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: η_Carnot = 1 − (T_cold_K / T_hot_K); COP_heating = T_hot_K / (T_hot_K − T_cold_K).
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Carnot Efficiency & COP via η_Carnot = 1 − (T_cold_K / T_hot_K); COP_heating = T_hot_K / (T_hot_K − T_cold_K).

Frequently Asked Questions

What equation powers the Carnot Heat Engine Thermal Efficiency & Heat Pump / Refrigerator COP Calculator?

It evaluates η_Carnot = 1 − (T_cold_K / T_hot_K); COP_heating = T_hot_K / (T_hot_K − T_cold_K) using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Thermodynamics & Heat Transfer

Carnot Heat Engine Thermal Efficiency & Heat Pump / Refrigerator COP Calculator: inputs, method, and how to read the result

Find theoretical maximum Carnot efficiency, Heat Pump COP, and Chiller COP.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Hot Reservoir Kelvin: Hot source absolute temperature (T_H) in Kelvin.
  • Cold Reservoir Kelvin: Cold sink absolute temperature (T_C) in Kelvin.
  • Heat Input Kw: Thermal power input (Q_H) in kilowatts.

What the calculation includes

With the default values shown, Carnot Maximum Thermal Efficiency is 53.85 %. The calculation follows Carnot Efficiency & COP Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Hot Reservoir Kelvin from 650 K to 715 K changes Carnot Maximum Thermal Efficiency from 53.85 % to 58.04 %. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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