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Joule-Thomson Cryogenic Cooling Calculator engineering
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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 $\Delta T$
--
K (cooling across valve)
Outlet Temperature $T_2$
--
K (after expansion)
J-T Coefficient $\mu_{JT}$
--
K / bar (@ $T_1$)
Max Inversion Temp $T_{inv}$
--
K (zero-pressure limit)
Liquefaction Fraction $y$
--
% liquid produced
Net Cooling Power $\dot{Q}_c$
--
Watts (refrigeration)

Joule-Thomson Inversion Curve ($P$ vs $T$)

Temperature $T$ (K) Pressure $P$ (bar) COOLING REGION ($\mu_{JT} > 0$) HEATING REGION
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.

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