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Engineering · Thermodynamics

Polytropic Gas Compression and Expansion Work Calculator

Calculate a closed ideal-gas polytropic end pressure and boundary work from entered end volumes.

Engineering · Thermodynamics

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Thermodynamics: polytropic visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.hotcoldheat flows across the entered resistance
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

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Understand the engineering model

What this calculator is for

Calculate a closed ideal-gas polytropic end pressure and boundary work from entered end volumes. The workflow keeps every assumed property, state and coefficient visible so the result can be independently checked.

1Match the displayed relationship to the real system before entering data.
2Use one consistent unit basis and preserve absolute quantities where stated.
3Compare the intermediate results and retain the model boundary.

Visual explanation

The tailored schematic shows the direction of energy, signal, state change or reliability logic represented by the selected equation.

The governing relationship

p₂=p₁(V₁/V₂)ⁿ; W=(p₂V₂−p₁V₁)/(1−n), with W positive by the gas.

Keep the boundary visible

Quasi-equilibrium closed-system polytropic path; n=1, heat transfer, real-gas behavior and machine efficiency require separate treatment.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

p₂=p₁(V₁/V₂)ⁿ; W=(p₂V₂−p₁V₁)/(1−n), with W positive by the gas.

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

Compression to half the initial volume raises pressure according to the entered exponent and produces negative work by the gas.

p₂=p₁(V₁/V₂)ⁿ; W=(p₂V₂−p₁V₁)/(1−n), with W positive by the gas.

Supported inputs

Precision and limits

Analysis, not approval

Quasi-equilibrium closed-system polytropic path; n=1, heat transfer, real-gas behavior and machine efficiency require separate treatment.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.