Joule-Thomson Inversion Curve Calculator
Cryogenic Gas Liquefaction: Calculate the Joule-Thomson expansion coefficient ($\mu_{JT}$), inversion temperature curve ($T_{inv}$ vs $P$), and isenthalpic pressure drop cooling/heating.
Gas Properties & Expansion Conditions
JT Coefficient & Temperature Change
The Joule-Thomson Inversion Curve & Real Gas Thermodynamics
Throttling expansion cooling relies on intermolecular attractive forces (van der Waals forces) doing work against each other as gas molecules separate.
1. Mathematical Formulations
μ_JT = (∂T/∂P)_h = (1 / C_p) · [ T · (∂v/∂T)_p - v ] Van der Waals Fit: μ_JT ≈ (1 / C_p) · [ (2a / RT) - b ] Max Inversion Temp: T_inv,max = 2a / (R · b)
2. Key Gas Inversion Temperatures
- Nitrogen ($N_2$): $T_{inv} \approx 621\,\text{K}$ (cools upon expansion from room temperature).
- Hydrogen ($H_2$): $T_{inv} \approx 205\,\text{K}$ (must be pre-cooled with liquid nitrogen).
- Helium ($^4He$): $T_{inv} \approx 45\,\text{K}$ (must be pre-cooled with cryogenic Brayton/Stirling stages).
Frequently Asked Questions
What is the Joule-Thomson effect and inversion temperature?
The Joule-Thomson effect describes the temperature change of a real gas when it undergoes isenthalpic (constant enthalpy) expansion through a throttle valve or porous plug. The Joule-Thomson coefficient is defined as $\mu_{JT} = (\partial T / \partial P)_h$. If the gas temperature is below the maximum inversion temperature ($T < T_{inv}$), $\mu_{JT} > 0$ and the gas cools upon depressurization. Above $T_{inv}$, $\mu_{JT} < 0$ and expansion causes heating.
Why can helium and hydrogen NOT be liquefied by simple throttling at room temperature?
The maximum inversion temperature for helium is only $\approx 45\,\text{K}$ (and for hydrogen $\approx 205\,\text{K}$). If room temperature helium ($300\,\text{K}$) is throttled through a JT valve from $200\,\text{bar}$ down to $1\,\text{bar}$, it warms up rather than cooling! Helium must first be pre-cooled below $45\,\text{K}$ (typically to $\approx 15\sim 20\,\text{K}$ via liquid nitrogen and Stirling/GM engines) before the final JT expansion can liquefy it.
What is the Linde-Hampson liquefaction cycle?
The Linde-Hampson cycle compresses gas, removes the heat of compression with ambient water coolers, sends the high-pressure gas through a counter-flow recuperative heat exchanger, and expands it across a Joule-Thomson valve. The cold unliquefied gas flows backward through the heat exchanger, cooling incoming gas until liquid droplets condense at the valve outlet.