Here are the key steps to solve this problem:
1) Given: Initial diameter (D1) = 0.5 m
Initial pressure (P1) = 500 kPa
Final diameter (D2) = 0.55 m
2) The pressure is proportional to diameter. So we can write:
P/P1 = (D/D1)n
Where n is the proportionality constant.
3) Since the process is reversible, n = 1 (based on the property of reversible process where PV must be proportional to T).
4) Putting n = 1 in the above equation, we get:
P2/P1 = (D2/D1