2026-07-30 10 min

Compressor Discharge Temperature Calculator

Calculate compressor discharge temperature for various compression processes. Essential for material selection, cooling system design, and safety analysis.

Calculator

Unit System

Inlet Temperature (T₁) [°C]

Pressure Ratio (r_p)

Specific Heat Ratio (k)

Polytropic Efficiency [%]

Results

Normal

Discharge Temperature (T₂)

160.9°C

Outlet temperature after compression

Discharge Temperature (T₂)

434.0K

Outlet temperature in Kelvin

Temperature Rise (ΔT)

140.9K

Temperature increase across compressor

Temperature Ratio

1.5-

T₂/T₁ ratio

Isentropic T₂

128.1°C

Ideal isentropic discharge temperature

Safety Status

Safe-

Safety classification based on T₂

Visualizations

Results Overview

160.9°CDischarge Temperature

434°CDischarge Temperature

140.9°CTemperature Rise

1.5°CTemperature Ratio

128.1°CIsentropic T₂

Formula

Discharge temperature for polytropic compression. The polytropic efficiency accounts for irreversibilities that increase temperature rise.

T₂ = T₁ × (p₂/p₁)^((k-1)/(k×η_poly))

Alternative Form

T₂_is = T₁ × (p₂/p₁)^((k-1)/k)

Variables

Symbol	Name	Unit	Description
T₂	Discharge Temperature	°C / K	Outlet gas temperature
T₁	Inlet Temperature	°C / K	Inlet gas temperature
r_p	Pressure Ratio	-	p₂/p₁
k	Specific Heat Ratio	-	Cp/Cv
η_poly	Polytropic Efficiency	%	Compression efficiency

Explanation

Discharge temperature depends on pressure ratio, gas properties (k), and compression efficiency. Higher pressure ratios and lower efficiency both increase discharge temperature. For isentropic (ideal) compression, η = 1.0, giving the minimum temperature. Real compressors with η < 1 produce higher discharge temperatures.

Derivation

From the polytropic relationship pV^n = constant and ideal gas law pV = RT, we derive T₂/T₁ = (p₂/p₁)^((n-1)/n). The polytropic exponent n relates to k and efficiency: (n-1)/n = (k-1)/(k×η_poly). Combining gives the formula for polytropic discharge temperature.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Determine inlet conditions: temperature T₁ and pressure ratio r_p.

T₁:20 °C

r_p:3

Result: Inlet temperature = 20 °C, PR = 3

Step 2

Calculate the polytropic exponent using k and efficiency.

(n-1)/n = (k-1)/(k×η_poly)

k:1.4

η:80%

Intermediate: Exponent = 0.3571

Result: Polytropic exponent calculated

Step 3

Apply the polytropic temperature equation.

T₂ = T₁ × r_p^((k-1)/(k×η_poly))

T₁:20 °C

r_p:3

Result: T₂ = 160.9 °C (434.0 K)

Final Answer

160.9

Worked Examples

See how the calculator works with different scenarios.

Scenario

Air compressor with T₁=25°C, PR=4, k=1.4, η_poly=80%.

Inputs

T₁:25°C

PR:4

k:1.4

η:80%

Calculation

(n-1)/n = 0.4/(1.4×0.8) = 0.3571 T₂ = 298.15 × 4^0.3571 = 298.15 × 1.643 = 489.9 K = 216.7°C Isentropic T₂ = 298.15 × 4^0.286 = 298.15 × 1.486 = 443.0 K = 169.8°C

Result

T₂ = 216.7°C (Safety: Caution)

Interpretation

The polytropic discharge temperature is 216.7°C, which exceeds 180°C (Caution threshold). Consider improving efficiency or adding intercooling between stages.

Understanding Your Result

Your Result: Discharge Temperature (T₂): 160.9 °C

Typical range: Safe: <150°C. Caution: 150-200°C. Danger: >200°C. Material limits: Aluminum impellers 180°C, piston rings 150°C, mineral oil flash point ~200°C.

What This Means

Discharge temperature determines material selection, cooling requirements, and safety margins for compressor operation.

Why It Matters

Excessive discharge temperature damages piston rings, valve plates, seals, and lubricants. It can also create fire hazards with lubricating oil in air compressors. Most compressor standards limit T₂ to 200°C.

Professional Interpretation

The polytropic discharge temperature is ALWAYS higher than isentropic. The difference (T₂_actual - T₂_isentropic) represents the energy lost to irreversibilities and appears as excess heat. Monitoring this difference helps detect compressor degradation.

Recommendations

•Keep discharge temperature below 150°C for reliable long-term operation
•For temperatures above 180°C, use synthetic lubricants rated for high temperature
•Install temperature monitoring with alarms at 180°C and shutdown at 200°C
•Consider multistage compression with intercooling for PR > 4
•Monitor T₂ trend over time - increasing T₂ at constant PR indicates degradation

Educational Content

Introduction

Compressor discharge temperature is a critical operating parameter that affects material selection, lubrication, safety, and maintenance scheduling.

Concept Explanation

When gas is compressed, its temperature rises according to the thermodynamic process path. Isentropic compression (no heat transfer) gives the minimum temperature. Real compressors produce higher temperatures due to irreversibilities. The polytropic model accounts for both heat transfer and irreversibilities.

Applications

▸Material selection for compressor components

▸Lubricant selection and degradation analysis

▸Intercooler design and thermal management

▸Safety system design and alarm setpoints

▸Performance monitoring and degradation detection

Benefits

•Prevents material failure from overheating
•Optimizes intercooling system design
•Enables proper lubricant selection
•Provides early warning of compressor problems

Limitations

•Assumes constant k and η across the compression process
•Does not account for heat loss to cylinder walls
•Single-stage calculation only

Best Practices

•Monitor T₂ continuously for critical compressors
•Compare actual T₂ to isentropic T₂ to assess degradation
•Maintain intercoolers for maximum heat transfer
•Use temperature data for predictive maintenance scheduling

Common Misconceptions

Myth: Higher discharge temperature means more compression work is being done.

Truth: Higher T₂ at the same pressure ratio indicates inefficiency - the excess heat is wasted energy, not useful compression work.

Myth: Isentropic temperature is achievable with good cooling.

Truth: Even with perfect cooling, real compressors cannot achieve isentropic temperatures due to internal friction and turbulence.

Practical Tips

•A 10% decrease in polytropic efficiency increases T₂ by approximately 15-25°C at PR=4
•For every 10°C increase in T₁, T₂ increases by approximately 12-15°C (depends on PR and k)
•Helium (k=1.66) produces ~2× the temperature rise of air (k=1.4) at the same PR
•Synthetic lubricants are required when T₂ exceeds 180°C - mineral oil degrades rapidly
•Temperature rise per stage should be limited to 100-120°C for reciprocating compressors
•Install temperature sensors at each stage discharge for multistage compressors
•A rising T₂ trend with constant PR is one of the earliest indicators of compressor wear

Common Mistakes

Using isentropic instead of polytropic temperature formula

Always use the polytropic formula for real compressors. Isentropic gives the theoretical minimum, not the actual temperature.

Ignoring efficiency when calculating T₂

Include polytropic efficiency in the exponent. Using η=100% gives isentropic T₂, which may be 30-60°C lower than actual.

Confusing Celsius and Kelvin in the formula

Always convert to Kelvin (K = °C + 273.15) before calculation. A common error is using °C directly, which gives wrong results.

Not accounting for intercooling in multistage

For multistage compressors, calculate T₂ for each stage separately using the stage inlet temperature after intercooling.

Assumptions

This calculator makes the following assumptions to provide estimates:

Constant Gas Properties: Specific heat ratio k is assumed constant. In reality, k varies with temperature.

Constant Efficiency: Polytropic efficiency is constant across the compression process. Efficiency may vary with operating point.

Ideal Gas: Gas follows ideal gas law. Real gas corrections needed at high pressure.

No External Heat Transfer: The polytropic model only accounts for internal irreversibilities. External cooling or heating is not modeled.

Limitations

Be aware of these limitations when using this calculator:

Constant k Assumption: At very high temperatures (>300°C), k changes significantly. The formula becomes less accurate at extreme temperatures.

No Cooling Model: Does not account for cylinder cooling jackets or interstage cooling that reduce actual discharge temperature.

Single Point Calculation: Provides discharge temperature at a single operating point. For complete thermal analysis, consider the entire operating range.

No Gas Composition Effects: Gas mixtures require weighted k values. Condensation of components during compression can change gas composition.

Frequently Asked Questions

Answers to common questions about this calculator.

How do I calculate compressor discharge temperature?

Use T₂ = T₁ × (p₂/p₁)^((k-1)/(k×η_poly)). Convert temperatures to Kelvin, use absolute pressures.

What is a safe discharge temperature?

Below 150°C is safe for most compressors. 150-200°C requires caution (synthetic lubricants). Above 200°C is dangerous for most systems.

How does pressure ratio affect discharge temperature?

Higher PR increases T₂ exponentially. Doubling PR from 3 to 6 adds approximately 60-80°C to discharge temperature for air.

What is the difference between isentropic and polytropic T₂?

Isentropic T₂ is the ideal minimum. Polytropic T₂ is always higher, with the difference representing irreversibilities. The gap widens at higher PR and lower efficiency.

How does efficiency affect discharge temperature?

Lower efficiency increases T₂. A drop from 85% to 75% efficiency at PR=4 adds approximately 25-35°C to discharge temperature.

What is the maximum temperature for compressor materials?

Aluminum impellers: 180°C. Steel cylinders: 200°C. Piston rings: 150°C (standard), 250°C (special). Valve plates: 180°C. Mineral oil: 180°C flash point.

How does gas type affect discharge temperature?

Higher k (specific heat ratio) produces higher T₂. Helium (k=1.66) gives much higher temperatures than air (k=1.4) at the same PR.

When do I need intercooling?

When T₂ exceeds 180°C, or when PR > 4 for air compressors. Intercooling reduces the suction temperature for subsequent stages.

How do I calculate T₂ for multistage compressors?

Calculate each stage separately. Stage 1: T₁ to T₂. After intercooling, T₁ for stage 2 is the intercooler outlet temperature. Repeat for each stage.

What is the dew point of compressed air?

After compression and cooling, water vapor condenses. The dew point depends on inlet humidity and pressure. Higher PR increases the dew point temperature.

How does altitude affect discharge temperature?

Altitude affects only through inlet temperature (which is lower at altitude). The PR calculation uses absolute pressures.

What is the effect of humidity on T₂?

Water vapor has a higher specific heat than air. High humidity slightly reduces the effective k value, which slightly reduces discharge temperature.

How do I measure discharge temperature accurately?

Use thermocouples or RTDs inserted into the gas stream. Shield the sensor from radiation from hot surfaces. Allow for thermal mixing length downstream.

What causes high discharge temperature?

Worn valves (leakage), worn piston rings, fouled intercoolers, increased PR, reduced efficiency, or incorrect gas properties.

How does speed affect discharge temperature?

Higher speed increases friction losses and reduces volumetric efficiency, both of which increase discharge temperature.

What is the temperature limit for oil-flooded screw compressors?

Oil-flooded screw compressors typically limit discharge temperature to 100-110°C to prevent oil degradation. Oil acts as a coolant.

How do I estimate the cooling load from discharge temperature?

Cooling load = ṁ × Cp × (T₂ - T_desired). Use the mass flow rate and specific heat to calculate the heat that must be removed.

What is the thermal efficiency penalty of high T₂?

Higher T₂ means more energy is carried away as waste heat. Each 10°C above isentropic represents approximately 2-3% efficiency loss.

Can I use the ideal gas law at high temperatures?

At high temperatures (>300°C), the ideal gas assumption becomes more accurate, not less. Real gas deviations are more significant at low temperatures and high pressures.

How does discharge temperature affect valve life?

Valve life decreases exponentially with temperature. At 180°C, valve life is approximately half that at 120°C. High temperature accelerates material fatigue.

Related Calculators

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Compressor Temperature Management Guide

API guidelines for temperature control in compressors

Understanding Discharge Temperature

CAGI educational resources on compressor temperatures

Lubricant Selection for High-Temperature Compressors

Lubrication best practices for elevated temperatures

Glossary

Technical terms used in mortgage calculations explained in plain language.

Polytropic Efficiency: Ratio of polytropic work to actual work, accounting for heat transfer and irreversibilities.
Isentropic Process: Reversible adiabatic process with no heat transfer - gives minimum temperature rise.
Polytropic Exponent (n): Exponent in pV^n = constant for real compression processes.
Discharge Temperature: Temperature of gas at compressor outlet after compression.
Intercooling: Cooling gas between compression stages to reduce temperature.
Specific Heat Ratio (k): Cp/Cv - determines temperature sensitivity to pressure change.
Dew Point: Temperature at which water vapor begins to condense from compressed air.
Flash Point: Temperature at which lubricant vapor can ignite - critical safety parameter.

Authoritative References

Trusted sources and standards referenced by this calculator.

API 617 - Axial and Centrifugal Compressors API 618 - Reciprocating Compressors ASME PTC 10 - Compressors Performance Test ISO 1217 - Displacement Compressor Test GPSA Engineering Data Book

Applicable Standards

API 617API 618ASME PTC 10ISO 1217ISO 5389

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.