Polytropic Process Calculator
Polytropic work is (p₁V₁ − p₂V₂)/(n − 1): compressing 0.1 m³ of air from 100 to 800 kPa with n = 1.3 gives W = -20.5289 kJ (negative: work done on the gas).
n = 1 isothermal, n = γ adiabatic.
-20.5288714676382 kJ
Full answer, then cut to fewer decimals (not rounded):
- -20.5288714676382 kJ
- -20.528871467638 kJ
- -20.52887146763 kJ
- -20.5288714676 kJ
- -20.528871467 kJ
- -20.52887146 kJ
- -20.5288714 kJ
- -20.528871 kJ
- -20.52887 kJ
- -20.5288 kJ
- -20.528 kJ
- -20.52 kJ
- -20.5 kJ
- Final volume V₂
- 0.0201983 m³
- Final temperature T₂
- 484.76 K
- Heat transfer Q
- -5.13222 kJ
- Change in internal energy ΔU = Q − W
- 15.3967 kJ
- Sign
- negative: work is done on the gas (compression)
Step-by-step solution
- pVⁿ = C → V₂ = V₁ (p₁/p₂)^(1/n) = 0.0201983 m³
- W = (p₁V₁ − p₂V₂)/(n − 1) = (10 − 16.1587) ÷ 0.3 = -20.5289 kJ
- Q = W (γ − n)/(γ − 1) = -5.13222 kJ
Polytropic Process Formula
W = (p₁V₁ − p₂V₂)/(n − 1), Q = W(γ − n)/(γ − 1)
pVⁿ = constant; n = 1 isothermal W = p₁V₁ ln(V₂/V₁)
Worked Example
Air compressed from 100 kPa, 0.1 m³, 300 K to 800 kPa with n = 1.3:
- pVⁿ = C → V₂ = V₁ (p₁/p₂)^(1/n) = 0.0201983 m³
- W = (p₁V₁ − p₂V₂)/(n − 1) = (10 − 16.1587) ÷ 0.3 = -20.5289 kJ
- Q = W (γ − n)/(γ − 1) = -5.13222 kJ
Final temperature T₂: 484.76 K · Heat transfer Q: -5.13222 kJ · Change in internal energy ΔU = Q − W: 15.3967 kJ · Sign: negative: work is done on the gas (compression)
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Frequently asked questions
What values of n give the common processes?
n = 0 constant pressure, n = 1 isothermal, n = γ reversible adiabatic and n → ∞ constant volume.
Why is heat rejected in polytropic compression with n < γ?
Q = W(γ − n)/(γ − 1); with W negative and n < γ, Q is negative, so heat leaves the gas.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Polytropic Process Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/polytropic-process-calculator/
IEEE
Scientific Converters, "Polytropic Process Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/polytropic-process-calculator/