How to calculate initial and final temperatures during supercritical steam expansion?
Since supercritical steam is not an ideal gas, you might want to use standard reference data (e.g. provided by NIST).  

Initial state
mass m0 = 10 kg
pressure p0 = 500 bar = 50.0 MPa
volume V0 = 0.01 m3
density ρ0 = 1000 kg/m3
temperature T0 = 340.53 K
specific enthalpy h0 = 323.06 kJ/kg  

Final state
mass m1 = 10 kg
pressure p1 = 500 bar = 50.0 MPa
volume V1 = 0.07 m3
density ρ1 = 142.86 kg/m3
temperature T1 = 925.86 K
specific enthalpy h1 = 3453.11 kJ/kg  

Heat transfer
heat Q = ΔH = (h1 – h0) • m = 31.3 MJ