BIZOMAT MAKEOS · Pneumatics
Closed Gas Vessel Temperature Check (Pressure Rise, Contents, Fill Limit)
If this closed gas vessel or cylinder heats up, how high does its pressure rise, is it within the rating, and what is the highest pressure I can fill it to?
Pressure change of a fixed volume of gas with temperature: the pressure at the hot condition from the gas law at constant volume (as the gas law tool with equal volumes), the mass of gas held, the pressure rise against the vessel rating or relief setting, and the highest fill pressure at the filling temperature that keeps the hot pressure within the rating.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Vessel volume | L | Internal volume of the vessel. |
| Fill pressure (gauge) | bar | Gauge pressure when filled. |
| Temperature at filling | °C | Gas temperature at filling. |
| Highest temperature in service | °C | Highest gas temperature in service (sun, process heat, fire case). |
| Atmospheric pressure | bar | Atmospheric pressure. |
| Gas constant | J/kg·K | Specific gas constant (287 air, 297 nitrogen, 2077 helium). |
| Vessel rating or relief setting (gauge) | bar | Maximum allowable working pressure or relief setting. |
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: Vessel volume
- What it is
- The internal (water) volume of the closed vessel or cylinder that holds the gas.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 10000000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the mass of gas held, not the pressures.
- Get it right
- Litres; 1 m³ = 1000 L.
What this means: Fill pressure (gauge)
- What it is
- The gauge pressure in the vessel when it was filled, read at the filling temperature.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Gauge pressure; the tool adds atmospheric pressure for the gas law.
What this means: Temperature at filling
- What it is
- The temperature of the gas at the moment it was filled to the fill pressure.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -60 °C to 300 °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.
- Get it right
- Gas temperature, which can be higher than ambient straight after fast filling.
What this means: Highest temperature in service
- What it is
- The highest temperature the gas could reach in service, for example from sun, process heat or a fire case.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -60 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The hot pressure rises in proportion to the absolute temperature (°C + 273.15).
What this means: Atmospheric pressure
- What it is
- The local atmospheric pressure, used to convert the gauge pressures into absolute pressures for the gas law.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.5 bar to 1.2 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.
What this means: Gas constant
- What it is
- The specific gas constant of the gas in the vessel: the universal gas constant divided by the gas’s molar mass. It is used only for the mass of gas held.
- Units and format
- Enter a number in J/kg·K: J/kg·K. The form accepts 50 J/kg·K to 5000 J/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 287 J/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Specific constant in J/kg·K, not the universal 8.314 J/mol·K.
What this means: Vessel rating or relief setting (gauge)
- What it is
- The maximum allowable working pressure of the vessel, or the relief valve setting, from the nameplate or design documents.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 2000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 230 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Gauge pressure, on the same basis as the fill pressure.
Method and formulas
- Constant volume: P₂ = P₁ T₂ ÷ T₁ in absolute units (as the gas law tool with V₂ = V₁).
- Mass m = P₁ V ÷ (R T₁).
- Highest fill pressure = (rating + p_atm) × T₁ ÷ T₂ − p_atm.
- Example: filled to 200 bar at 20 °C, the vessel reaches 227.43 bar at 60 °C against 230 bar; fill to at most 202.26 bar.
Limitations
- Ideal gas; at very high pressures use a compressibility factor.
- Uniform gas temperature; the vessel itself is taken as rigid.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an air or nitrogen vessel left in the sun
- Set the fill pressure for a gas spring or accumulator
- Check a sealed enclosure for heating
Who it is for
- Design engineers
- Maintenance engineers
- Safety engineers
What you get
- Pressure at the hot condition
- Mass of gas
- Rating check and the highest fill pressure
Interpreting the result
- Pressure rises about one third of a percent per kelvin at room temperature: a 40 K rise adds about 14%.
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
Temperature, the hidden leak
In Production Leak Testing by the Numbers
What it covers: Why hundredths of a kelvin swamp a pressure decay test, fill heating and its time constant, warm parts, compensation and its limits, and a line move that caused 18% false rejects.
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.
Open the Closed Gas Vessel Temperature Check (Pressure Rise, Contents, Fill Limit) calculator