Originally Posted by airtren
Pointing that Thrust needs to be considered, or explaining that your calculated approx 4200 ft height's discrepancy of 1700ft is due to Drag, or Thrust, means including Drag or Thrust a second time in the equation.
That's not correct.
Nevertheless, henra seems correct to me also.
Beside speed, altitude is not the only parameter changing during the climb, the flight equilibrum is also changed (thrust/drag ratio).
If no additional power is applied for an altitude change, the aircraft needs more lift; alpha will be increased and airframe will produce more drag. A lesser factor is the loss of thrust at same RPM due to increased flight level.
Consequently, no matter if the calculation is based on IAS or TAS, energy state change is not only due to a single altitude parameter changing while your estimation is only factoring altitude on it.