Steps for iterative calculation(refer Shigley Section 3-14):
The max stress will occur at the inside surface. So stress calculations below will be done at the inside radius.
1. Assume possible OD of tube
2. Calculate circumferential stress (sigma_t)
3. Calculate radial stress(sigma_r)
4. Calculate axial stress (sigma_a, inside pressure*inside area/tube cross-sectional area )
5. Calculate von-Mises stress sigma_v (ref wikipedia)
6. Find the yield stress of pure copper, sigma_y (33 MPa from internet)
7. If sigma_v>sigma_y then increase the outside diameter, and so on....
I used Matlab for iterative calculation and got 12 mm OD(6 mm outside radius). So the thickness is 2 mm.