CO2 heat exchanger information required

[Hods]

On one side of the heat exchanger I am flowing -40 degrees C liquid CO2 at 8 litres per minute. On the other side of the heat exchanger I am counter flowing a carbon dioxide vapor from -20 degrees C with the same mass per minute as the other side of the exchanger and need to bring it down to -40 degress C (liquid). I know that 100% is not possible so I was hoping to throttle the -40 CO2 going into the heat exchanger to create -50 degrees C, then the as long as the heat exchanger would bring the temp within 10 dregrees of the other side.

Will this work in Theory?

Also if I am using 1/2" steel pipe (condensing line)for the outer casing and 3/8" copper tubing for the inside of the heat exchanger, how many square feet of copper surface area would I need for this amount of heat transfer?

Thank you for any help you are able to provide.