The thermodynamic property used to determine the amount of work produced by a power turbine in a heat engine is:

Enthalpy

Explanation:

Thermodynamic properties could be Intensive or extensive properties. Intensive properties are those that don't depend on the quantity of matter. Examples are pressure & temperature. Meanwhile, extensive properties are those whose values depend on the mass of the system. Examples are Energy, enthalpy and volume.

Now, in turbines in thermodynamics, the work done is produced by the flow required to turn the turbine and shaft. Recall that from the law of conservation of energy, the work in the turbine per mass airflow would be equal to the change in specific enthalpy of the flow from the entrance to the exit point of the turbine.

Thus, the property required to determine the work is Enthalpy.