Carnot Efficiency Calculator

Understanding Carnot Efficiency Calculator

The Carnot efficiency is the maximum possible efficiency for a heat engine operating between two temperatures. No real engine can exceed it.

How to use this calculator

1. Enter the hot reservoir temperature, \(T_H\), in an absolute scale such as kelvin.
2. Enter the cold reservoir temperature, \(T_C\), in the same unit.
3. Click calculate to find the Carnot efficiency, \(\eta_{Carnot}\).
4. Read the result as a decimal or a percent, and compare it with real engine performance.

The formula explained

The formula \(\eta_{Carnot} = 1 - \frac{T_C}{T_H}\) computes the maximum possible efficiency for a heat engine operating between a hot source and a cold sink. The temperatures must be absolute temperatures, because the ratio only works correctly on that scale.

• \(\eta_{Carnot}\) = the maximum theoretical efficiency of the heat engine
• \(T_H\) = temperature of the hot reservoir
• \(T_C\) = temperature of the cold reservoir

Step by step method

1. Write down the hot and cold temperatures in the same absolute unit, usually kelvin.
2. Divide \(T_C\) by \(T_H\).
3. Subtract that ratio from \(1\) to get the efficiency.
4. If needed, multiply by \(100\) to convert the decimal to a percent.

Worked example

Problem. A heat engine operates between \(T_H = 600\,\text{K}\) and \(T_C = 300\,\text{K}\). What is its Carnot efficiency?

1. Compute the ratio, \(\frac{T_C}{T_H} = \frac{300}{600} = 0.5\).
2. Use the formula, \(\eta_{Carnot} = 1 - 0.5 = 0.5\).
3. Convert to a percent, \(0.5 = 50\%\).

Tips and common mistakes

• Use kelvin, not degrees Celsius, because Carnot efficiency depends on absolute temperature.
• If \(T_C\) is close to \(T_H\), the efficiency will be low, and if \(T_C \ge T_H\), the formula does not describe a valid heat engine.

Frequently asked questions