Question

A turbine operates at steady state, and experiences a heat loss. 1.1 kg/s of water flows through the system. The inlet is maintained at 100 bar, 520 Celsius. The outlet is maintained at 10 bar, 280 Celsius. A rate of heat loss of 60 kW is measured. Determine the rate of work output from the turbine, in kW.

Answer 1

`\dot W_(out) = 399.47\,kW`

Step-by-step explanation:

The turbine is modelled after the First Law of Thermodynamics:

`-\dot Q_(out) -\dot W_(out) + \dot m\cdot (h_(in)-h_(out)) = 0`

The work done by the turbine is:

`\dot W_(out) = \dot m \cdot (h_(in)-h_(out))-\dot Q_(out)`

The properties of the water are obtained from property tables:

Inlet (Superheated Steam)

`P = 10\,MPa`

`T = 520\,^(\textdegree)C`

`h = 3425.9\,(kJ)/(kg)`

Outlet (Superheated Steam)

`P = 1\,MPa`

`T = 280\,^(\textdegree)C`

`h = 3008.2\,(kJ)/(kg)`

The work output is:

`\dot W_(out) = \left(1.1\,(kg)/(s)\right)\cdot \left(3425.9\,(kJ)/(kg) -3008.2\,(kJ)/(kg)\right) - 60\,kW`

`\dot W_(out) = 399.47\,kW`