BIZOMAT MAKEOS · Pneumatics
Gas Compression and Expansion Process
What final volume, temperature and work result from compressing or expanding this gas?
Final volume and temperature and the work for isothermal, adiabatic or polytropic compression or expansion of a gas between two absolute pressures.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Process | choice | How heat is exchanged during the process. |
| Initial pressure (absolute) | bar | Absolute starting pressure (1.013 bar at sea level for free air). |
| Initial volume | L | Starting volume. |
| Initial temperature | °C | Starting temperature. |
| Final pressure (absolute) | bar | Absolute final pressure. |
| Ratio of specific heats k | k = cp/cv (1.4 for air and nitrogen). | |
| Polytropic exponent n | Polytropic exponent for the polytropic process (between 1 and k for cooled compressors). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Process
- What it is
- How heat flows while the gas is compressed or expanded: kept at constant temperature (isothermal), with no heat exchange (adiabatic) or in between (polytropic).
- Units and format
- Choose one of 3 options from the list: Isothermal (n = 1); Adiabatic (n = k); Polytropic (n as entered).
- Example
- The form opens with “Adiabatic (n = k)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Only the adiabatic process uses k and only the polytropic process uses n.
What this means: Initial pressure (absolute)
- What it is
- The absolute pressure of the gas before the process starts, measured from vacuum, not from atmosphere.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 10000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.013 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Add atmospheric pressure to a gauge reading: absolute = gauge + atmospheric.
What this means: Initial volume
- What it is
- The volume of gas at the start of the process, at the initial pressure and temperature, such as a cylinder volume or a quantity of free air.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The final volume and the work are directly proportional to the starting volume.
- Get it right
- Enter litres; 1 m³ = 1000 L.
What this means: Initial temperature
- What it is
- The temperature of the gas at the start of the process.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273 °C to 3000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The final absolute temperature is proportional to the starting absolute temperature.
- Get it right
- Enter °C; the tool converts to kelvin for the calculation.
What this means: Final pressure (absolute)
- What it is
- The absolute pressure of the gas at the end of the process. Higher than the start for compression, lower for expansion.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 10000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Add atmospheric pressure to a gauge reading: absolute = gauge + atmospheric.
What this means: Ratio of specific heats k
- What it is
- The ratio of the gas’s specific heat at constant pressure to that at constant volume, cp ÷ cv, from gas property tables.
- Units and format
- Enter a plain number with no unit. The form accepts 1.01 to 1.67. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher k gives a higher final temperature in adiabatic compression.
- Get it right
- Used only for the adiabatic process.
What this means: Polytropic exponent n
- What it is
- The exponent in pVⁿ = constant describing a real process between isothermal (n = 1) and adiabatic (n = k), from test data or your compressor reference.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher exponent gives a higher final temperature in compression.
- Get it right
- Used only for the polytropic process.
Method and formulas
- p₁V₁ⁿ = p₂V₂ⁿ, with n = 1 (isothermal), k (adiabatic) or as entered.
- T₂ = T₁ (p₂/p₁)^((n − 1)/n) (kelvin).
- Work (closed system): isothermal p₁V₁ ln(p₂/p₁); otherwise (p₂V₂ − p₁V₁) ÷ (n − 1).
- Example: adiabatic compression of 100 L of air from 1.013 to 8 bar abs ends at 255.92 °C in 22.853 L.
Limitations
- Ideal gas; real compressors also have valve losses and leakage.
- Closed-system (non-flow) work; for steady-flow compressor work see the compressor power tool.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate discharge temperature of a compressor
- Find work and volume for an air spring or accumulator
- Compare isothermal and adiabatic behaviour
Who it is for
- Process engineers
- Maintenance engineers
- Design engineers
What you get
- Final volume
- Final temperature
- Work done on (or by) the gas
Interpreting the result
- High adiabatic temperatures show why compressors need intercooling and aftercooling.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3032–3041. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
The work of compression and specific power
In Compressed Air Plant by the Numbers
What it covers: Calculate the isothermal and isentropic work to compress CA-1's air, compare its 41 kW against them, price a cubic metre of air, and compare compressors on a fair basis.
Method explained here · BIZOMAT original book
Compressor work and discharge temperature
In Process Chillers by the Numbers
What it covers: Ideal and real compression from NIST data, isentropic efficiency, why R-134a heats less than air, motor losses, discharge temperature, and a starved evaporator.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.