A steam turbine operates with 1.6 MPa and 350°C steam at its inlet and saturated vapor at 30°C at its exit. The mass flow rate of the steam is 22 kg/s, and the turbine produces 12,350 kW of power. Determine the rate at which heat is lost through the casing of this turbine.

638.8kW

Explanation:

The flow rate of the steam m = 22kg/s

The Pressure of the steam at the inlet of the turbine P1 = 1.6MPa

The temperature of the steam at the inlet of the turbine T1 = 350*C

Steam quality at the exit of the turbine x2 = 1.0

The temperature of the steam at the exit of the turbine T2 = 30*C

Power produced = 12,350kW

Assuming the turbine is running on a steady state, hence we neglect the effect of kinetic and potential energy we get:

If you refer to the superheated steam table for the specific enthalpy at a pressure of 1.6MPa and temperature of 350*C, we get

h1 = 3,146kJ/kg

Refer to the steam table for saturated gas at temperature 30*C to get the specific enthalpy value h2 = 2,556.81kJ/kg

The heat that comes out from the turbine can be defined from the balance of energy in the system, and is represented as

Ein - Eout = change in system Energy = 0

Thus Ein = Eout

mh1 = mh2 + Wout + Qout

Qout = m (hi-h2) - Wout

Qout = 22 x (3146-255.6) - 12350

Qout = 638.8kW