What a kilogram gives up
Strip the steady-flow energy equation down to a turbine and almost everything cancels: no heat crosses the casing worth counting, and the velocity terms are small. What is left is the enthalpy drop. Read aloud: w equals h-one minus h-two — , where is the enthalpy at the stop valve in kJ/kg, is the enthalpy leaving the last stage in the same units, and is the specific work, the work taken from every single kilogram. Subscript 1 is always the inlet, 2 always the exhaust, everywhere in this chapter.
Then scale it up: — P equals m-dot w. (the dot means per unit time) is the steam mass flow in kg/s, and is the shaft power at the coupling. Push the units through and the arithmetic explains itself: kJ/kg × kg/s leaves kJ/s, and a kilojoule per second is a kilowatt. That cancellation is the entire units stage of this lesson, done in your head.
Units guide, they never confess. If a rearrangement's units refuse to cancel into kW, the rearrangement is wrong and there is no appeal. Units that do work out prove nothing at all — the check runs one way only.