Thermal Pressure Calculator

Calculator

Example data table

Formulas used

1) Ideal gas at constant volume

When volume and gas amount stay constant, pressure follows absolute temperature:

P₂ = P₁ · (T₂/T₁)     and     ΔP = P₂ − P₁

2) Real gas at constant volume (Z correction)

A simple compressibility-factor correction uses Z values at each state:

P₂ = P₁ · (T₂/T₁) · (Z₂/Z₁)

3) Thermoelastic bulk pressure in a rigid container

For a material prevented from changing volume, a common estimate is:

P_th = K · α_v · ΔT     and     P₂ = P₁ + P_th

4) Restrained solid thermal stress

A basic restrained estimate uses a constraint factor C:

σ = C · E · α_L · ΔT

This tool also supports an optional relaxation percentage to reduce σ when assemblies are not perfectly rigid.

Technical guide and practical data

1) What “thermal pressure” means

Thermal pressure is the pressure (or stress) change caused by a temperature change when expansion is restricted. In a sealed gas volume, temperature raises molecular energy, increasing pressure. In a rigid liquid-filled container, thermal expansion fights compressibility. In restrained solids, thermal strain becomes mechanical stress.

2) Model selection by real constraint

Use the constant‑volume gas models for sealed vessels where volume does not change. Use the bulk model for fluids or materials in near‑rigid volumes (pipe segments with closed valves, filled cavities, test cells). Use the restrained solid model for components bolted, welded, or captured so free expansion is prevented.

3) Typical parameter ranges

Order‑of‑magnitude values help with quick checks: steel E ≈ 200 GPa, aluminum E ≈ 69 GPa; metals often have αL ≈ 10–25×10⁻⁶ 1/K. Many liquids have αv around 10⁻⁴–10⁻³ 1/K, while bulk modulus K can be hundreds of MPa to a few GPa.

4) Why Kelvin matters in gas calculations

Gas pressure ratios require absolute temperature. For example, heating from 20 °C to 80 °C changes temperature from 293.15 K to 353.15 K, so P₂/P₁ ≈ 1.205. That is about a 20.5% pressure rise at constant volume, before any real‑gas correction.

5) Real‑gas Z option for higher pressures

At elevated pressures or near condensation, ideal behavior can drift. The Z‑factor correction provides a simple improvement when Z data is available: P₂ = P₁·(T₂/T₁)·(Z₂/Z₁). If you do not have Z, setting Z₁ = Z₂ = 1 keeps results consistent with the ideal model.

6) Interpreting restrained‑solid stress

Thermal stress estimates are sensitive to restraint. This calculator offers uniaxial, biaxial, and triaxial approximations using Poisson ratio ν. A relaxation percentage lets you model partial stress relief from slip, creep, or yielding. Treat these results as screening values, then validate with design standards where needed.

7) Unit practice and reporting

Engineering teams often mix kPa, MPa, bar, atm, and psi. The multi‑unit table helps prevent conversion mistakes and supports documentation. The history log captures timestamped inputs and outputs so you can reproduce results, compare scenarios, and export clean CSV or PDF summaries.

8) Safety and design context

Thermal pressure can exceed component ratings quickly in confined systems. Always compare predicted pressures with allowable limits, include safety margins, and consider relief devices where applicable. If the temperature rise is uncertain, run worst‑case values and record the assumptions for traceability.

FAQs

1) Which model should I use for a closed gas tank?

Choose the constant‑volume gas model. Use the Z‑factor option if the gas is at high pressure or you have compressibility data. Always enter temperatures in the selected unit; the tool converts to Kelvin internally.

2) I do not know Z. What should I enter?

Set Z1 and Z2 to 1.0. That reproduces ideal‑gas behavior. If you later obtain Z values from a chart or dataset, you can rerun the case and compare the difference in P2 and ΔP.

3) What does the bulk model represent physically?

It estimates pressure rise when a material wants to expand with temperature but is confined by a nearly rigid volume. The calculation uses Pth = K·αv·ΔT, where K captures compressibility and αv captures thermal expansion.

4) Can I enter compressibility instead of bulk modulus?

Yes. Switch bulk input mode to β, then provide β and its unit. The tool converts β to K using K = 1/β, then applies the same thermal‑pressure relation to compute Pth and the final pressure.

5) Why can restrained‑solid results look very large?

Perfect restraint converts thermal strain directly into stress. Real parts often relieve stress through slip, creep, or yielding. Use the relaxation setting for partial relief and treat the output as a conservative estimate unless validated by detailed analysis.

6) What if I leave baseline pressure P1 empty?

For bulk and solid modes, the calculator will report the thermal contribution as the primary result. For gas models, P1 is required because the method computes a final pressure from an initial state and a temperature ratio.

7) How accurate are the presets?

Presets are typical values intended for quick checks and learning. Materials vary by grade, temperature, and state. For engineering decisions, replace presets with verified datasheet values and record the source in your report exports.