Calculator Inputs
Example Data Table
These examples assume air, γ = 1.40, cp = 1.005 kJ/kg·K, inlet temperature = 288.15 K, and efficiency = 85%.
| Case | Pressure Ratio | Ideal Exit Temp K | Actual Exit Temp K | Actual Work kJ/kg |
|---|---|---|---|---|
| Low boost | 2.00 | 351.2 | 362.3 | 74.5 |
| Medium compressor | 4.00 | 428.1 | 452.8 | 165.5 |
| High pressure stage | 8.00 | 522.1 | 563.4 | 276.5 |
Formula Used
Ideal isentropic outlet temperature:
T₂s = T₁ × rₚ^((γ − 1) / γ)
Actual compressor outlet temperature:
T₂ = T₁ + (T₂s − T₁) / ηc
Polytropic outlet temperature:
T₂p = T₁ × rₚ^((γ − 1) / (γ × ηp))
Pressure ratio from measured outlet temperature:
rₚ = [(T₁ + ηc × (T₂ − T₁)) / T₁]^(γ / (γ − 1))
Specific compressor work:
w = cp × (T₂ − T₁)
Temperatures must use absolute units inside the formula. This page converts Celsius, Fahrenheit, and Rankine before solving.
How to Use This Calculator
- Select the calculation mode that matches your task.
- Enter inlet temperature and choose its unit.
- Enter pressure ratio, gas heat capacity ratio, and efficiency values.
- Use measured exit temperature only for reverse calculations.
- Set a pressure ratio range for the comparison table.
- Press Calculate to display the result above the form.
- Download the CSV or PDF file for reporting.
Compressor Exit Temperature and Pressure Ratio Guide
Why Exit Temperature Matters
Compressor exit temperature is a key design value in thermodynamics. It affects material limits, cooling demand, lubrication, and downstream safety. A higher pressure ratio usually raises the exit temperature. The rise is not linear. It depends on gas properties and compression efficiency. Engineers use this value when sizing intercoolers, turbines, ducts, and process equipment. Operators also track it to detect fouling, worn blades, leakage, or poor cooling.
Using Pressure Ratio Wisely
Pressure ratio is outlet absolute pressure divided by inlet absolute pressure. Gauge pressure should be converted to absolute pressure before use. The calculator accepts direct pressure ratio because that avoids pressure unit confusion. For ideal compression, entropy is assumed constant. Real machines need more work, so actual exit temperature is higher. Isentropic efficiency corrects the ideal temperature rise. Lower efficiency means more heat appears for the same pressure ratio.
Interpreting Efficiency
Air compressors, gas turbines, turbochargers, and process compressors may use different efficiency definitions. Isentropic efficiency compares ideal work with actual work. Polytropic efficiency treats compression as many small stages. It is useful for high pressure ratios and multi-stage machines. This calculator shows both estimates so you can compare assumptions. Use measured discharge temperature when testing real equipment. Then solve efficiency or pressure ratio and compare the answer with design data. Always confirm inlet temperature, gas composition, and sensor calibration before making decisions.
Practical Notes
For dry air near room temperature, γ is often close to 1.40. The value changes with gas type and temperature. Specific heat also changes at high temperature. For precision work, use property tables or software. For early design and classroom checks, this tool gives a fast and transparent estimate. The downloadable table helps compare many pressure ratios in one report.
FAQs
1. What is compressor exit temperature?
It is the gas temperature at the compressor outlet. It is higher than inlet temperature because compression adds work to the gas.
2. What pressure ratio should I enter?
Enter absolute outlet pressure divided by absolute inlet pressure. Do not divide gauge pressures unless you first convert them to absolute pressures.
3. Why is actual temperature higher than ideal temperature?
Real compressors have losses. Efficiency below 100% means extra work becomes additional heat, so actual discharge temperature rises above the ideal value.
4. What is a normal gamma value for air?
Dry air near ordinary conditions often uses γ = 1.40. Hot gases, steam, refrigerants, and mixtures need their own gas property values.
5. Can this calculator handle Celsius input?
Yes. The page converts Celsius, Fahrenheit, and Rankine to Kelvin internally. The formulas require absolute temperature units.
6. What does polytropic mode do?
Polytropic mode estimates compression as many small steps. It is often preferred for multi-stage compressors and large pressure ratio comparisons.
7. What is specific compressor work?
Specific work is the energy added per kilogram of gas. This calculator estimates it as cp multiplied by the actual temperature rise.
8. Can I export my results?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a clean report containing the result and tables.