Ideal Gas Compressor Power Discharge Temperature Calculator

The Ideal Gas Compressor Power and Discharge Temperature Calculator works out what it takes to compress an ideal gas from one absolute pressure to another. It returns the pressure ratio, the isentropic discharge temperature, the selected-model discharge temperature, the temperature rise, the specific work on both the isentropic and the selected basis, and the shaft power at the mass flow you enter.

It runs on one of two bases. The ideal isentropic branch fixes the compressor efficiency at exactly one and reports the thermodynamic minimum. The efficiency-adjusted branch divides that work by an isentropic efficiency you enter, and puts the difference into the gas as heat, so the discharge temperature rises with it.

Every gas property is yours to supply. The specific heat at constant pressure and the heat capacity ratio gamma are both typed in, with no property lookup and no inference from gas identity. The shipped values are synthetic demonstration numbers, not table values.

It accepts SI metric entry in kilopascals absolute, degrees Celsius, kilograms per second and kilowatts, or U.S. customary entry in psia, degrees Fahrenheit, pounds mass per second and horsepower. Changing the selector relabels the fields; it does not convert numbers already entered.

Three limits matter before you use a number from it. Both pressures must be absolute, and a gauge entry is silently wrong. There is no compressibility factor anywhere in the model, so the gas is ideal throughout. And the power reported is gas-path shaft work only, with motor, gearbox and auxiliary losses outside it.

Purpose and model boundary

This model estimates discharge temperature, specific work and shaft power for steady adiabatic compression of an ideal gas with user-entered constant heat capacity and heat-capacity ratio. It offers an ideal isentropic branch and an efficiency-adjusted branch. It is a thermodynamic screening model, not a compressor map, driver selection or equipment guarantee.

The spreadsheet is the calculation authority. The browser submits named inputs through the calculation service and renders the workbook's returned values, chart and status; it does not reproduce compressor formulas client-side.

Inputs and units

Temperatures are converted to kelvin and US quantities to SI internally. Pressure inputs must be absolute, not gauge values.

Governing relationships

For pressure ratio PR = p2/p1 and exponent a = (γ − 1)/γ, the isentropic temperature is

T2s = T1 × PR^a.

The active efficiency is ηactive = 1 for the ideal branch and the entered η for the efficiency-adjusted branch. The selected discharge temperature, isentropic and required specific work, and powers are

• T2 = T1 + (T2s − T1)/ηactive;
• ws = cp(T2s − T1);
• w = ws/ηactive;
• Pisentropic = ṁws;
• Prequired = ṁw.

The workbook's chart evaluates the same selected-model temperature expression at seven pressure-ratio points from 1 through the entered PR; it is not an equipment operating curve.

Calculation sequence

1. Validate the unit and model choices, positive absolute pressures with p2 ≥ p1, inlet temperature above absolute zero, nonnegative mass flow, positive cp, γ > 1, and active efficiency in (0,1].
2. Convert temperature, mass flow and heat capacity to the SI calculation basis.
3. Calculate PR, the isentropic exponent, T2s, selected T2, specific work and power.
4. Convert results to the selected display units.
5. Check that public values, positivity relationships and chart points are finite and internally consistent.
6. Return the model-basis label, temperature curve and ordered workbook status.

Outputs and interpretation

Primary outputs are selected discharge temperature, isentropic discharge temperature, required specific work and required shaft power. Details expose pressure ratio, temperature rise, isentropic work and power, and the active model basis. The ideal branch makes selected and isentropic results equal. The efficiency-adjusted branch increases temperature rise and work when η < 1.

Required shaft power is the modeled gas-path requirement. Motor input, gearbox, seal, bearing, cooling and auxiliary requirements need separate efficiencies and margins.

Validation and status logic

The workbook evaluates status in this order:

The equal-pressure check takes precedence over the zero-flow check when both conditions apply.

Assumptions and limitations

• The gas is ideal; compression is steady and adiabatic; kinetic and potential energy changes are negligible.
• Entered cp and γ are constant and representative of the whole temperature range. No gas composition or property lookup is supplied.
• The adjusted branch treats η as one aggregate isentropic compressor efficiency.
• Variable heat capacity, real-gas compressibility, condensation, chemical reaction, heat leakage, intercooling, aftercooling, multistage optimization and polytropic-map methods are outside scope.
• No surge, choke, speed line, corrected flow, corrected speed, efficiency island or discharge-temperature limit is embedded.
• Materials, lubrication, seals, vibration, critical speed, containment, relief, hazardous service and code compliance require separate review.

Restrictions and non-computing states

The model supports compression only: p2/p1 ≥ 1. Expansion, vacuum pumping below a pressure ratio of one, liquids and two-phase states are outside scope. Temperature must remain above absolute zero, γ must exceed one, and active efficiency must be greater than zero. A NOT VALID state supersedes displayed residues. Equal pressure and zero mass flow are deliberate computing boundaries with CHECK messages.

Errors and warnings

A rejected entry means the submission did not satisfy the published input rules. NOT VALID means the workbook refused the state; CHECK identifies a defined zero-work or zero-power boundary. Calculation-service failures are availability errors, not thermodynamic conclusions.

No compressor map, selection table, licensed gas property database or compressibility chart is reproduced. The calculator performs no property lookup: cp and the heat capacity ratio are user-entered, and the shipped values are synthetic demonstration numbers describing no particular gas. The workbook implements the ordinary textbook form of the ideal-gas isentropic compression relations, not the method of any single publication. The sources it cites are below.

• NASA Glenn Research Center, Compressor Thermodynamics, for the pressure ratio, the ideal-gas isentropic temperature ratio, specific work as cp times the temperature rise, and the efficiency-adjusted work relation. https://www.grc.nasa.gov/www/k-12/airplane/compth.html
• NASA Glenn Research Center, Compression and Expansion, for the ideal-gas isentropic pressure-temperature exponent. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/compression-and-expansion/
• NIST Guide to the SI, Appendix B, for the exact pound-mass, pressure and mechanical-horsepower identities used in U.S. customary mode. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors
• NIST Guide to the SI, Chapter 8, for the kelvin, Celsius and Fahrenheit relations and temperature intervals. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8

Gas properties, compressibility factors, polytropic exponents and efficiencies, mechanical efficiencies, compressor maps, surge limits, allowable discharge temperatures and driver margins are not supplied here. Take them from a property source for your gas and from the manufacturer. Near the critical point or at high reduced pressure, redo the case with a real-gas equation of state.

Additional source notes migrated from Methodology

• NASA Glenn, Compressor Thermodynamics — pressure ratio, ideal-gas isentropic temperature ratio and efficiency-adjusted compressor work.
• NASA Glenn, Compression and Expansion — independent public derivation of the isentropic pressure-temperature relation.
• NIST Guide to the SI, Appendix B and Chapter 8 — exact public unit and temperature-scale identities.
• NBSIR 81-2401 and NIST Handbook 133, Appendix E — exact Btu_IT and avoirdupois identities used by the US path.

Gas-property justification, the compressor vendor's map and qualified thermodynamic and mechanical review govern real compressor selection.