Carnot Efficiency Calculator Formula

Understand the math behind the carnot efficiency calculator. Each variable explained with a worked example.

Formulas Used

Carnot Efficiency

efficiency = 1 - cold_temp / hot_temp

Efficiency (%)

efficiency_pct = (1 - cold_temp / hot_temp) * 100

Variables

VariableDescriptionDefault
hot_tempHot Reservoir Temperature(K)600
cold_tempCold Reservoir Temperature(K)300

How It Works

Carnot Efficiency

The Carnot efficiency is the theoretical maximum efficiency any heat engine can achieve operating between two temperatures.

Formula

eta = 1 - T_cold / T_hot

Temperatures must be in Kelvin. No real engine can exceed this efficiency due to the second law of thermodynamics.

Worked Example

A heat engine operating between 600 K and 300 K.

hot_temp = 600cold_temp = 300
  1. 01eta = 1 - Tc/Th
  2. 02eta = 1 - 300/600
  3. 03eta = 1 - 0.5
  4. 04eta = 0.5 = 50%

Frequently Asked Questions

Can any real engine achieve Carnot efficiency?

No. The Carnot efficiency represents an ideal, reversible process. All real engines have irreversible losses (friction, heat leaks) and operate below this limit.

How can efficiency be improved?

Increase the hot temperature or decrease the cold temperature. This is why power plants use superheated steam and cold cooling water.

What is a typical power plant efficiency?

Modern coal plants: 33-45%. Gas turbines with combined cycle: up to 62%. All below their respective Carnot limits.

Learn More

Guide

Thermodynamics Basics: A Complete Guide

Learn the fundamentals of thermodynamics including the four laws, heat transfer, entropy, enthalpy, and the Carnot cycle. Practical explanations with real-world examples.

Ready to run the numbers?

Open Carnot Efficiency Calculator