Joule-Thomson Cryogenic Cooling Calculator
Cryogenics & thermodynamics: Calculate Joule-Thomson isenthalpic expansion cooling ($\Delta T$), the J-T coefficient ($\mu_{JT}$), inversion temperature ($T_{inv}$), and Linde-Hampson liquefaction fraction.
Gas & Expansion Parameters
Throttling Cooling & Liquefaction
J-T Temperature Drop $\Delta T$
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K (cooling across valve)
Outlet Temperature $T_2$
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K (after expansion)
J-T Coefficient $\mu_{JT}$
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K / bar (@ $T_1$)
Max Inversion Temp $T_{inv}$
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K (zero-pressure limit)
Liquefaction Fraction $y$
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% liquid produced
Net Cooling Power $\dot{Q}_c$
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Watts (refrigeration)
Joule-Thomson Inversion Curve ($P$ vs $T$)
Expansion cools only inside the parabolic inversion envelope ($\mu_{JT} > 0$). Expanding a gas outside the inversion curve causes heating!
J-T Thermodynamics & Inversion Physics
The Joule-Thomson effect is an isenthalpic ($H = \text{const}$) throttling expansion through a valve or restriction. The Joule-Thomson coefficient $\mu_{JT}$ is defined by:
$$\mu_{JT} = \left( \frac{\partial T}{\partial P} \right)_H = \frac{1}{C_p} \left[ T \left( \frac{\partial V}{\partial T} \right)_P - V \right]$$
$$T_{inv,max} \approx \frac{2a}{Rb} \approx 6.75 \, T_c \quad (\text{Van der Waals approximation})$$
For Helium ($T_{inv} = 45 \text{ K}$) and Hydrogen ($T_{inv} = 205 \text{ K}$), inversion temperatures are far below room temperature. Expanding them from 300 K warms the gas, requiring precooling with liquid nitrogen before J-T expansion can produce liquid.