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

Answer:

$\dot W_{out} = 399.47\,kW$

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)

$P = 10\,MPa$

$T = 520\,^{\textdegree}C$

$h = 3425.9\,\frac{kJ}{kg}$

Outlet (Superheated Steam)

$P = 1\,MPa$

$T = 280\,^{\textdegree}C$

$h = 3008.2\,\frac{kJ}{kg}$

The work output is:

$\dot W_{out} = \left(1.1\,\frac{kg}{s}\right)\cdot \left(3425.9\,\frac{kJ}{kg} -3008.2\,\frac{kJ}{kg}\right) - 60\,kW$

$\dot W_{out} = 399.47\,kW$