# Cooling power of $\rm CO_2$ being released from a gas bottle

I need help in calculating how much a constant flow of CO2, being released into a small pipeline from a pressurised gas bottle, cools down the pipeline (in watts), to figure out if I'd need to heat up the pipes.

At the moment I think I know how to calculate the temperature of the released gas using an isentropic flow equation:

$P/P_t = (T/T_t)^{(k/(k-1))}$

I know both pressures ($P/P_t$), the temperature of the pressurised gas ($T_t$) and the ratio of specific heats of CO2 ($k$), but I'd like to know how the flow rate affects the cooling of the pipes.

Do i need to get into fluid mechanics and Heat transfer mechanisms to get an answer or do i use some kind of equation based on the Joule-Thomson effect?

Sorry if I'm being incomprehensible, this is my 1st post and english is my 2nd language.