Why is Carnot efficiency the maximum?
It is the efficiency of a reversible engine. The second law of thermodynamics forbids any engine from exceeding it between the same two temperatures.
Carnot Efficiency Calculator
η = 1 − T_c/T_h
Calculate the maximum (Carnot) efficiency of a heat engine. η = 1 − T_c/T_h, with temperatures in kelvin.
Calculate
Enter values above to calculate
How it calculates
1
Both temperatures must be in kelvin
2
η = 1 − T_c / T_h
3
Multiply by 100 for percentage
Formula
η = 1 − T_c/T_h
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| η | Carnot efficiency | dimensionless (0–1) |
| T_c | Cold reservoir temperature | K |
| T_h | Hot reservoir temperature | K |
How to Use This Calculator
This carnot efficiency calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula η = 1 − T_c/T_h is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A heat engine between 600 K and 300 K. Find maximum efficiency.
Step 1: η = 1 − T_c/T_h
Step 2: η = 1 − 300/600
Step 3: η = 1 − 0.5
Answer: η = 0.5 = 50% (theoretical maximum)
Common Mistakes
- Temperatures MUST be in kelvin — never Celsius
- Real engines are always less efficient than the Carnot limit
- 100% efficiency would require T_c = 0 K (impossible by the third law)
Related
Frequently Asked Questions
Can efficiency reach 100%?
Only if the cold reservoir is at absolute zero (0 K), which is unattainable. So real efficiency is always < 100%.