When a gas expands through an adiabatic throttle (often a porous plug), the temperature can change as a result of the Joule-Thomson effect. Select one of four gases and use sliders to adjust the inlet temperature, inlet pressure, and outlet pressure. The intensity of the red color is proportional to the pressure, and the throttle is thicker for a larger pressure drop. Select "J-T coeff. vs. temperature" to see the Joule-Thomson coefficient plotted as a function of temperature. If this simulation is too big or too small for your screen, zoom out or in using command - or command + on Mac or ctrl - or ctrl + on Windows.
The energy balance for an adiabatic throttle implies that
$$H_{out} = H_{in}.$$
The throttle does no work, and because the gas moves so quickly through the throttle, it does not have much time to transfer heat to the surroundings. The Joule-Thomson coefficient is derived by starting with the exact differential for enthalpy:
$$dH = \left(\frac{\partial H}{\partial P}\right)_T dP + \left(\frac{\partial H}{\partial T}\right)_P dT.$$
Since \(dH=0\) for a throttle, and the derivative of enthalpy \(H\) with respect to temperature \(T\) at constant pressure \(P\) is the heat capacity \(C_p,\) then:
$$-\left(\frac{\partial H}{\partial P}\right)_T dP = C_pdT.$$
Rearranging, and given that the enthalpy \(H\) is constant,
$$-\left(\frac{\partial H}{\partial P}\right)_T = C_p \left(\frac{\partial T}{\partial P}\right)_{H}, $$
where \(\left(\frac{\partial T}{\partial P}\right)_H = \mu_{JT},\) and \(\mu_{JT}\) is the Joule-Thomson coefficient. Integration then relates the output temperature to the inlet temperature and the pressure drop:
$$T_{out} = T_{in} + \mu_{JT}(P_{out}-P_{in}).$$
If \(\mu_{JT}\) > \(0,\) the outlet temperature is lower than the inlet temperature. If \(\mu_{JT}\) < \( 0,\) then the outlet temperature is higher.
This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Jackson Dunlap under the direction of Professor John L. Falconer and Michelle Medlin, with the assistance of Neil Hendren and Drew Smith. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Adam J. Johnston and Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.