I need to calculate the amount of power needed in a heat exchanger to make up for heat loss due to high pressure gas expanding across a valve at a constant flow rate, and a constant pressure upstream of the valve (p1) and down-stream of the valve (p2), P2 is constant due to a back pressure regulator down stream of the valve. I am only interested in the heat loss due to the primary expansion (2850 --> 400) The volumes upstream of the valve and down stream of the valve are not changing as the gas is being fed at a constant rate from an infinite supply source.
The gas is CO2, p1 =2850 psi, p2 = 400 psi, T1=40C. I would like to keep the down stream temperature at 25C.