Calculating heat absorbed from expanding gas I'm trying to calculate the amount of heat absorbed per kg of different types of gas, namely compressed air and carbon dioxide. Starting with carbon dioxide, I found that the Joule-Thompson coefficient varies between 1.16 x 10^-5 and 0.23 x 10^-5 K/Pa, depending on the pressure. In addition, the specific heat of carbon dioxide changes depending on temperature, so which value should I use for each of these? And so far this doesn't even take into account the latent heat of vaporization, how do I add that in? The CO2 will be going from a 30C, 7 MPa liquid to a 1 KPa gas.
 A: The Joule-Thompson coefficient is defined as $\left(\frac{\partial T}{\partial P}\right)_H$.  For a pure substance, a change in enthalpy is determined by:
$$dH=C_pdT+\left[V-T\left(\frac{\partial V}{\partial T}\right)_P\right]dP$$  You can solve this equation for the Joule Thompson coefficient by setting dH equal to zero.  When you apply the equation, you need to use the heat capacity and the bracketed term at the temperature and pressure of the gas.  Both the temperature and pressure changes in the JT are assumed to occur differentially.
In the JT experiment, it is assumed that the change takes place adiabatically with a pressure drop through a valve or porous plug.  If you are interested in finite changes in pressure, you still assume that the operation takes place adiabatically (Q = 0), and that the change in enthalpy per unit mass passing through the device is zero.  You then determine the finite change in temperature resulting from a finite change in pressure, holding the enthalpy constant.  This is most easily done using thermodynamic diagrams for a material, such a P-H diagram.
