adiabatic expansion of CO2 - rate of cooling

mattbanham90

Hi Physics forum,

I have a pipe which is of length L, inner diameter D. It is packed with CO2 at pressure P (assume it's still a gas with none of this funny supercritical business!) and temperature T. The density of the CO2 is rho and the joule-kelvin coefficient is mu. the pipe is initially sealed at both ends. However, it suddenly breaks at one end (in an infinitesimally small time). The gas is set to emerge into the atmosphere at a high rate. However, JT cooling of the gas causes some of it to freeze.

My questions are:

1.) what is the rate of cooling of the CO2 (ignoring freezing for now) in terms of the parameters above?

2.) what is the rate of freezing of the gas?

3.) will the pipe freeze up and seal preventing further CO2 from escaping?

4.) if so, how much gas escapes before it freezes up and how long does it take before it seals?

If anyone has any pointers to this then fantastic.

Matt