Calculator
Choose a mode, enter values, and calculate. Temperatures must be absolute for the Carnot relation, so inputs are converted internally to Kelvin.
Formula Used
Th = Tc / (1 − η), and Tc = Th (1 − η). Temperatures are internally converted to Kelvin for consistency.
How to Use This Calculator
- Select a calculation mode that matches your goal.
- Enter the required temperature(s) and choose units.
- If solving for temperature, enter a target efficiency value.
- Optionally add Qin and Qout to estimate work and compare efficiencies.
- Press Calculate to view results above the form.
- Use the CSV or PDF buttons to save results.
Example Data Table
Sample values show the ideal limit for different reservoir temperatures (absolute scale).
| Th (K) | Tc (K) | η (fraction) | η (%) |
|---|---|---|---|
| 600 | 300 | 0.5000 | 50.00 |
| 900 | 300 | 0.6667 | 66.67 |
| 1200 | 400 | 0.6667 | 66.67 |
| 750 | 290 | 0.6133 | 61.33 |
Article
1) Why Carnot efficiency matters
Carnot efficiency sets the theoretical ceiling for any heat engine operating between a hot reservoir and a cold reservoir. It depends only on absolute temperatures, not on the working fluid or the machine design. Engineers use it to judge how far a real cycle is from the reversible limit.
2) The temperature difference drives work
With the Carnot relation, raising the hot-side temperature or lowering the cold-side temperature increases the maximum possible fraction of heat that can become work. For example, Th = 900 K and Tc = 300 K gives η = 1 − 300/900 = 0.6667, meaning at best 66.67% of heat input can be converted.
3) Absolute temperature is non‑negotiable
Because η uses a ratio, temperatures must be expressed on an absolute scale. This calculator accepts common units and converts them internally to Kelvin. A frequent mistake is using Celsius differences directly; 600 °C and 300 °C are not a valid pair for the formula unless converted to absolute values.
4) Typical ranges in practice
Modern steam power plants may have hot-side temperatures on the order of 800–900 K, while cooling water or ambient sinks often sit near 290–310 K. These values suggest an ideal limit around 60–65%, yet real overall efficiencies are commonly lower due to irreversibilities and component losses.
5) Refrigerators and heat pumps
The same temperature limits constrain reverse devices. While this page focuses on engine efficiency, the idea is identical: the closer the device operates to reversible behavior, the closer it approaches the maximum performance dictated only by Th and Tc. Large temperature lifts demand more input energy.
6) Connecting efficiency to heat and work
If you provide heat input Qin, the calculator estimates the maximum possible work Wmax = η · Qin. For instance, Qin = 1200 kJ with η = 0.50 yields Wmax = 600 kJ. Adding Qout lets you compute actual work W = Qin − Qout and compare an actual efficiency to the limit.
7) Interpreting the “gap” to Carnot
The gap ηCarnot − ηActual is a quick diagnostic. A small gap suggests a highly optimized cycle, while a large gap indicates strong irreversibilities such as friction, heat leaks, finite temperature gradients, pressure drops, and non‑ideal compression or expansion. The gap cannot be negative if measurements are consistent.
8) Using the calculator for design checks
Use the “solve for temperature” modes to plan feasibility. If a target efficiency is demanded, the tool can compute the required hot temperature for a given sink temperature, or the required sink temperature for a given hot source. This is useful for early-stage concepts, cooling strategy decisions, and reporting.
FAQs
1) What does Carnot efficiency represent?
It is the maximum possible efficiency of a heat engine operating reversibly between a hot reservoir Th and a cold reservoir Tc. Real engines must be lower.
2) Why must temperatures be absolute?
The formula uses the ratio Tc/Th. Only absolute scales (Kelvin or Rankine) preserve meaningful ratios. The calculator converts from Celsius and Fahrenheit automatically.
3) Can Carnot efficiency ever reach 100%?
No, unless Tc approaches 0 K, which is unattainable. Any finite Tc gives Tc/Th > 0, so η < 1.
4) What if Tc is greater than Th?
That violates the heat-engine assumption and would imply negative efficiency. The calculator flags this and asks for a hot temperature greater than the cold temperature.
5) How is maximum work calculated?
When you enter Qin, the tool computes Wmax = η · Qin using the Carnot η from the selected mode. This is an ideal upper bound.
6) What do Qin and Qout add to the analysis?
They let you compute actual work W = Qin − Qout and an actual efficiency W/Qin. You can then compare that value to the Carnot limit.
7) Why is real efficiency always lower?
Real cycles have irreversibilities: friction, heat transfer across finite temperature differences, pressure losses, and non‑ideal compression/expansion. These destroy available work, reducing efficiency below the reversible limit.