Calculator · Thermal Engineering
Polytropic Process Calculator
A quasi-equilibrium ideal-gas process that follows pvⁿ = constant. One index covers constant pressure (n = 0), constant temperature (n = 1) and reversible adiabatic (n = γ). Constant volume is its own mode here, never an infinite n.
Inputs
Pressure is absolute (from vacuum) and temperature is absolute (kelvin). No atmospheric pressure is added and no Celsius value is converted behind the scenes.
Results
Boundary work W (by the gas)
ΔU = Q − W. Q > 0 is heat added to the gas; W > 0 is boundary work done by the gas on its surroundings, so a compression has W < 0.
| Process | General polytropic |
|---|---|
| Polytropic index n | 1.3 |
| Property | State 1 | State 2 |
|---|---|---|
| p (abs) | 100 kPa | 800 kPa |
| T | 300 K | 484.76 K |
| v | 0.861 m³/kg | 0.17391 m³/kg |
| Boundary work W (by the gas) | -176.75 kJ |
|---|---|
| Heat Q (into the gas) | -44.188 kJ |
| ΔU | 132.57 kJ |
| ΔH | 185.59 kJ |
| First-law residual Q − W − ΔU | 0 J |
Assumptions
- · ideal gas
- · constant specific heats
- · quasi-equilibrium closed system
Explore in the Lab
The full process state travels; the Lab adds the P–v diagram.
Technical reference
p vⁿ = const, T2/T1 = (v1/v2)ⁿ⁻¹
W = m R (T2 − T1)/(1 − n), n ≠ 1
W = m R T1 ln(V2/V1), n = 1
ΔU = m cv ΔT, ΔH = m cp ΔT, Q = ΔU + W
- n
- polytropic index[-]
- W
- boundary work done by the gas[J]
- Q
- heat added to the gas[J]
- γ
- cp/cv[-]
ΔU = Q − W. Q > 0 is heat added to the gas; W > 0 is boundary work done by the gas on its surroundings, so a compression has W < 0.
With n = 0 a final pressure cannot fix the end state, so the volume ratio must be used.
Defaults: 100 kPa, 300 K air compressed with n = 1.3.