Polytropic Compression Calculator
Calculate final pressure, temperature and boundary work for a closed ideal-gas polytropic volume change.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply PV^n=constant and the ideal-gas temperature relation. Use the logarithmic work limit when n is one.
P₂=P₁(V₁/V₂)^n; T₂=T₁(V₁/V₂)^(n−1); work on gas=−∫P dV
Worked example
For an isothermal change n=1 from 1 L to 0.1 L at initial 100 kPa, final pressure is 1000 kPa and work on the gas is 100 ln(10)≈230.258509 J.
Assumptions and input details
Closed fixed-mass ideal gas, quasistatic path with constant entered exponent; n=1 uses isothermal work. Positive work is on the gas. Heat transfer, nonideal behavior and flow-compressor shaft work are not inferred.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
The 36 volume definitions distinguish US liquid, US dry and Imperial measures. Cups carry an explicit definition. Japanese shō is 2401/1331 L and a gō is one tenth of it; the explicitly labelled 180 mL rice cup is separate.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · UK Imperial definitions · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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